XII Convegno su Problemi di Fisica Nucleare Teorica
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Maria Colonna Laboratori Nazionali del Sud (Catania)
Nuclear Matter and Nuclear Dynamics Nuclear Matter and Nuclear Dynamics
XII Convegno su Problemi di Fisica Nucleare TeoricaCortona 8-10 Ottobre 2008
The EOS of symmetric and neutron matter from many-body theoriesThe EOS of symmetric and neutron matter from many-body theoriesthe energy functional is calculated from the bare nucleon-nucleon interaction
Information on EInformation on Esymsym behavior from Heavy Ion Collisions behavior from Heavy Ion Collisions Transport theories
High density EOS High density EOS implications on the structure of neutron starsimplications on the structure of neutron stars
Transition to the QGP Transition to the QGP Role of isospin
Microscopic three-body force(TBF) exchange diagrams on the basis of mesons incorporating Δ Ropernucleon-antinucleon excitations
BBG calculations with two- and three-body forcesBBG calculations with two- and three-body forcesThe energy functional is calculated from the bare nucleon-nucleon interaction
TBF consistent with the underlying two-nucleon One Boson Exchange potential
Results for EOS and symmetry energy
Li Lombardo Schulze Zuo PRC 2008
Bonn BNijmejen potential Argonne v18 potentialphenomenological Urbana type TBF
Constraints on pressure from nuclear flow data analysis
The overall effect of the same TBF on the EOS can be different according to the two-body force adopted
Stiffer EOS with TBF
EOS symm matterPhenomenological Urbana type TBF
Bonn B
v18
Similar EOS
BaldoShaban PLB661(08)
Li Lombardo Schulze Zuo PRC77(08)
EOS of Symmetric and Neutron MatterEOS of Symmetric and Neutron Matter
Dirac-BruecknerRMFDensity-Dependent couplings
Symmetric Matter | Symmetry Energy | Neutron Matter
DD-F
NLρ
NLρδ
Constraints from compact stars amp heavy ion dataTKlaehn et al PRC 74 (2006) 035802
Slope at normal densityIsospin transport at Fermi energies
BOB
Urbana
AFDMC
asy-soft
asy-stiff
Effective parameterizationsof symmetry energy
Transport codesNuclear Dynamics
Astrophysical problems
SGandolfi et al PRL98(2007)102503
Extracting information on the symmetry energy Extracting information on the symmetry energy from terrestrial labs from terrestrial labs
Fermi energies 10-60 MeVA (below and around normal density) GDR Charge equilibration Fragmentation in exotic systems
Intermediate energies 01-05 GeVA (above normal density) Meson production (pions kaons) Collective response (flows)
Nuclear DynamicsNuclear Dynamics
High density behavior Neutron stars
Transport equations
Phys Rep 389 (2004)
PhysRep410(2005)335
( ) ( ) ( ) ( ) ( )K r p t K r p t p p r r r t t
fWWfdtdf
Ensemble average
Langevin randomwalk in phase-space
Semi-classical approach to the many-body problemTime evolution of the one-body distribution function ( )f r p t
Boltzmann
)()()()()( tprKfKprffhprft
LangevinVlasov
Vlasov Boltzmann Langevin
)(2
)(2
fUm
pfhi
i
Vlasov mean field
Boltzmann average collision term
( ) ( ) NNf i f i
dp p E Ed
3 3 32 1 2
2 1 23 3 3( ) (12 1 2 )d p d p d pW r p f f f wh h h
Loss term
D(pprsquor)
SMF model fluctuations projected onto ordinary space density fluctuations δρ
Fluctuation variance σ2f = ltδfδfgt
D(pprsquor) w
Collective excitations
Charge equilibration
Relativistic nuclear excitation of GDRin the target in semi-peripheral collisions
Equations of motion for n and p centroids obtained from Einsteinrsquos set- Restoring force- Coulomb + nuclear excitation (Wood-Saxon)
Zrel = zn ndash zpXrel = xn - xp
T(b) attenuation factor due to depopulation of reaction channelsP(b) probability for a given reaction channel
DassoGallardoLanzaSofia NPA801(2008)129
(neutron skin)Larger amplitude due to nuclear field
one-phonon
two-phonon
212
2
1
1210 RR
ZN
ZN
AZZD
D(t) bremss dipole radiation CN stat GDRInitial Dipole
Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics
- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion
Symmetry energy below saturation
36Ar + 96Zr40Ar + 92Zr
BMartin et al PLB 664 (2008) 47
Experimental evidence of the extra-yield LNS data
Isospin gradients Pre-equilibrium dipole emission
SPIRALS rarr Collective Oscillations
22
3
2
)(3
2
DA
NZEc
edEdP
Bremsstrahlung Quantitative estimations
VBaran DMBrink MColonna MDi Toro PRL87(2001)
iDKD
pNZ
PPPtDK
xNZ
XtXtXA
NZtD
npinpnp
npinpnp
1)(
1)()()(
TDHF CSimenel PhChomaz Gde France
132Sn + 58Ni 124Sn + 58Ni
Larger restoring force with asy-soft larger strength arXiv08074118
b=8f
m
ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV
SMF - transport modelcalculations
experimental data (B Tsang et al PRL 92 (2004) )
Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and
Imbalance ratios
x = β = (N-Z)A
τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation
M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn
Kinetic energy loss
L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn
Time
JRizzo et al NPA806 (2008) 79
Several isoscalarinteractions
Unstable dynamics
Liquid-gas phase transitionFragmentation in exotic systems
Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm
Sn124 + Sn124 EA = 50 MeVA
Central collisions
Ni + Au EA = 45 MeVA
(fluctuations projected on ordinary space)
Isospin-dependent liquid-gas phase transition
Isospin distillation the liquid phase is more symmetric than the gas phase
β = 02
β = 01
Non-homogeneous density
asy-stiff - - -asy-soft
Density gradients derivative of Esym
asy-soft
asy-stiff
Spinodal decomposition in a box (quasi-analytical calculations)
β = 02
β = 01
NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo
Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606
arXiv07073416
arXiv07073416Cluster density
asy-soft
asy-stiff
Sn112 + Sn112
Sn124 + Sn124
b = 6 fm 50 AMeV
Isospin migration in neck fragmentationIsospin migration in neck fragmentation
Transfer of asymmetry from PLF and TLF to the low density neck region
Effect related to the derivative of the symmetryenergy with respect to density
PLF TLFneckemittednucleons
ρ1 lt ρ2
Asymmetry flux
asy-stiff
asy-soft
Larger derivative with asy-stiff larger isospin migration effects
Density gradients derivative of Esym
EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007
Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics
LNS data ndash CHIMERA coll
VrelVViola (IMFPLF)
(IMFTLF)
JRizzo et al NPA806 (2008) 79
Reactions at intermediate energies
Information on high density behaviorof Esym
scattering nuclear interaction from meson exchange main channels (plus correlations)
Isoscalar Isovector
Attraction amp Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ
ρψψˆ
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
21ˆˆ
41ˆˆˆ
21ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space
Esym= kin + (vector) ndash ( scalar)
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
The EOS of symmetric and neutron matter from many-body theoriesThe EOS of symmetric and neutron matter from many-body theoriesthe energy functional is calculated from the bare nucleon-nucleon interaction
Information on EInformation on Esymsym behavior from Heavy Ion Collisions behavior from Heavy Ion Collisions Transport theories
High density EOS High density EOS implications on the structure of neutron starsimplications on the structure of neutron stars
Transition to the QGP Transition to the QGP Role of isospin
Microscopic three-body force(TBF) exchange diagrams on the basis of mesons incorporating Δ Ropernucleon-antinucleon excitations
BBG calculations with two- and three-body forcesBBG calculations with two- and three-body forcesThe energy functional is calculated from the bare nucleon-nucleon interaction
TBF consistent with the underlying two-nucleon One Boson Exchange potential
Results for EOS and symmetry energy
Li Lombardo Schulze Zuo PRC 2008
Bonn BNijmejen potential Argonne v18 potentialphenomenological Urbana type TBF
Constraints on pressure from nuclear flow data analysis
The overall effect of the same TBF on the EOS can be different according to the two-body force adopted
Stiffer EOS with TBF
EOS symm matterPhenomenological Urbana type TBF
Bonn B
v18
Similar EOS
BaldoShaban PLB661(08)
Li Lombardo Schulze Zuo PRC77(08)
EOS of Symmetric and Neutron MatterEOS of Symmetric and Neutron Matter
Dirac-BruecknerRMFDensity-Dependent couplings
Symmetric Matter | Symmetry Energy | Neutron Matter
DD-F
NLρ
NLρδ
Constraints from compact stars amp heavy ion dataTKlaehn et al PRC 74 (2006) 035802
Slope at normal densityIsospin transport at Fermi energies
BOB
Urbana
AFDMC
asy-soft
asy-stiff
Effective parameterizationsof symmetry energy
Transport codesNuclear Dynamics
Astrophysical problems
SGandolfi et al PRL98(2007)102503
Extracting information on the symmetry energy Extracting information on the symmetry energy from terrestrial labs from terrestrial labs
Fermi energies 10-60 MeVA (below and around normal density) GDR Charge equilibration Fragmentation in exotic systems
Intermediate energies 01-05 GeVA (above normal density) Meson production (pions kaons) Collective response (flows)
Nuclear DynamicsNuclear Dynamics
High density behavior Neutron stars
Transport equations
Phys Rep 389 (2004)
PhysRep410(2005)335
( ) ( ) ( ) ( ) ( )K r p t K r p t p p r r r t t
fWWfdtdf
Ensemble average
Langevin randomwalk in phase-space
Semi-classical approach to the many-body problemTime evolution of the one-body distribution function ( )f r p t
Boltzmann
)()()()()( tprKfKprffhprft
LangevinVlasov
Vlasov Boltzmann Langevin
)(2
)(2
fUm
pfhi
i
Vlasov mean field
Boltzmann average collision term
( ) ( ) NNf i f i
dp p E Ed
3 3 32 1 2
2 1 23 3 3( ) (12 1 2 )d p d p d pW r p f f f wh h h
Loss term
D(pprsquor)
SMF model fluctuations projected onto ordinary space density fluctuations δρ
Fluctuation variance σ2f = ltδfδfgt
D(pprsquor) w
Collective excitations
Charge equilibration
Relativistic nuclear excitation of GDRin the target in semi-peripheral collisions
Equations of motion for n and p centroids obtained from Einsteinrsquos set- Restoring force- Coulomb + nuclear excitation (Wood-Saxon)
Zrel = zn ndash zpXrel = xn - xp
T(b) attenuation factor due to depopulation of reaction channelsP(b) probability for a given reaction channel
DassoGallardoLanzaSofia NPA801(2008)129
(neutron skin)Larger amplitude due to nuclear field
one-phonon
two-phonon
212
2
1
1210 RR
ZN
ZN
AZZD
D(t) bremss dipole radiation CN stat GDRInitial Dipole
Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics
- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion
Symmetry energy below saturation
36Ar + 96Zr40Ar + 92Zr
BMartin et al PLB 664 (2008) 47
Experimental evidence of the extra-yield LNS data
Isospin gradients Pre-equilibrium dipole emission
SPIRALS rarr Collective Oscillations
22
3
2
)(3
2
DA
NZEc
edEdP
Bremsstrahlung Quantitative estimations
VBaran DMBrink MColonna MDi Toro PRL87(2001)
iDKD
pNZ
PPPtDK
xNZ
XtXtXA
NZtD
npinpnp
npinpnp
1)(
1)()()(
TDHF CSimenel PhChomaz Gde France
132Sn + 58Ni 124Sn + 58Ni
Larger restoring force with asy-soft larger strength arXiv08074118
b=8f
m
ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV
SMF - transport modelcalculations
experimental data (B Tsang et al PRL 92 (2004) )
Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and
Imbalance ratios
x = β = (N-Z)A
τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation
M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn
Kinetic energy loss
L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn
Time
JRizzo et al NPA806 (2008) 79
Several isoscalarinteractions
Unstable dynamics
Liquid-gas phase transitionFragmentation in exotic systems
Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm
Sn124 + Sn124 EA = 50 MeVA
Central collisions
Ni + Au EA = 45 MeVA
(fluctuations projected on ordinary space)
Isospin-dependent liquid-gas phase transition
Isospin distillation the liquid phase is more symmetric than the gas phase
β = 02
β = 01
Non-homogeneous density
asy-stiff - - -asy-soft
Density gradients derivative of Esym
asy-soft
asy-stiff
Spinodal decomposition in a box (quasi-analytical calculations)
β = 02
β = 01
NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo
Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606
arXiv07073416
arXiv07073416Cluster density
asy-soft
asy-stiff
Sn112 + Sn112
Sn124 + Sn124
b = 6 fm 50 AMeV
Isospin migration in neck fragmentationIsospin migration in neck fragmentation
Transfer of asymmetry from PLF and TLF to the low density neck region
Effect related to the derivative of the symmetryenergy with respect to density
PLF TLFneckemittednucleons
ρ1 lt ρ2
Asymmetry flux
asy-stiff
asy-soft
Larger derivative with asy-stiff larger isospin migration effects
Density gradients derivative of Esym
EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007
Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics
LNS data ndash CHIMERA coll
VrelVViola (IMFPLF)
(IMFTLF)
JRizzo et al NPA806 (2008) 79
Reactions at intermediate energies
Information on high density behaviorof Esym
scattering nuclear interaction from meson exchange main channels (plus correlations)
Isoscalar Isovector
Attraction amp Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ
ρψψˆ
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
21ˆˆ
41ˆˆˆ
21ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space
Esym= kin + (vector) ndash ( scalar)
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Microscopic three-body force(TBF) exchange diagrams on the basis of mesons incorporating Δ Ropernucleon-antinucleon excitations
BBG calculations with two- and three-body forcesBBG calculations with two- and three-body forcesThe energy functional is calculated from the bare nucleon-nucleon interaction
TBF consistent with the underlying two-nucleon One Boson Exchange potential
Results for EOS and symmetry energy
Li Lombardo Schulze Zuo PRC 2008
Bonn BNijmejen potential Argonne v18 potentialphenomenological Urbana type TBF
Constraints on pressure from nuclear flow data analysis
The overall effect of the same TBF on the EOS can be different according to the two-body force adopted
Stiffer EOS with TBF
EOS symm matterPhenomenological Urbana type TBF
Bonn B
v18
Similar EOS
BaldoShaban PLB661(08)
Li Lombardo Schulze Zuo PRC77(08)
EOS of Symmetric and Neutron MatterEOS of Symmetric and Neutron Matter
Dirac-BruecknerRMFDensity-Dependent couplings
Symmetric Matter | Symmetry Energy | Neutron Matter
DD-F
NLρ
NLρδ
Constraints from compact stars amp heavy ion dataTKlaehn et al PRC 74 (2006) 035802
Slope at normal densityIsospin transport at Fermi energies
BOB
Urbana
AFDMC
asy-soft
asy-stiff
Effective parameterizationsof symmetry energy
Transport codesNuclear Dynamics
Astrophysical problems
SGandolfi et al PRL98(2007)102503
Extracting information on the symmetry energy Extracting information on the symmetry energy from terrestrial labs from terrestrial labs
Fermi energies 10-60 MeVA (below and around normal density) GDR Charge equilibration Fragmentation in exotic systems
Intermediate energies 01-05 GeVA (above normal density) Meson production (pions kaons) Collective response (flows)
Nuclear DynamicsNuclear Dynamics
High density behavior Neutron stars
Transport equations
Phys Rep 389 (2004)
PhysRep410(2005)335
( ) ( ) ( ) ( ) ( )K r p t K r p t p p r r r t t
fWWfdtdf
Ensemble average
Langevin randomwalk in phase-space
Semi-classical approach to the many-body problemTime evolution of the one-body distribution function ( )f r p t
Boltzmann
)()()()()( tprKfKprffhprft
LangevinVlasov
Vlasov Boltzmann Langevin
)(2
)(2
fUm
pfhi
i
Vlasov mean field
Boltzmann average collision term
( ) ( ) NNf i f i
dp p E Ed
3 3 32 1 2
2 1 23 3 3( ) (12 1 2 )d p d p d pW r p f f f wh h h
Loss term
D(pprsquor)
SMF model fluctuations projected onto ordinary space density fluctuations δρ
Fluctuation variance σ2f = ltδfδfgt
D(pprsquor) w
Collective excitations
Charge equilibration
Relativistic nuclear excitation of GDRin the target in semi-peripheral collisions
Equations of motion for n and p centroids obtained from Einsteinrsquos set- Restoring force- Coulomb + nuclear excitation (Wood-Saxon)
Zrel = zn ndash zpXrel = xn - xp
T(b) attenuation factor due to depopulation of reaction channelsP(b) probability for a given reaction channel
DassoGallardoLanzaSofia NPA801(2008)129
(neutron skin)Larger amplitude due to nuclear field
one-phonon
two-phonon
212
2
1
1210 RR
ZN
ZN
AZZD
D(t) bremss dipole radiation CN stat GDRInitial Dipole
Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics
- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion
Symmetry energy below saturation
36Ar + 96Zr40Ar + 92Zr
BMartin et al PLB 664 (2008) 47
Experimental evidence of the extra-yield LNS data
Isospin gradients Pre-equilibrium dipole emission
SPIRALS rarr Collective Oscillations
22
3
2
)(3
2
DA
NZEc
edEdP
Bremsstrahlung Quantitative estimations
VBaran DMBrink MColonna MDi Toro PRL87(2001)
iDKD
pNZ
PPPtDK
xNZ
XtXtXA
NZtD
npinpnp
npinpnp
1)(
1)()()(
TDHF CSimenel PhChomaz Gde France
132Sn + 58Ni 124Sn + 58Ni
Larger restoring force with asy-soft larger strength arXiv08074118
b=8f
m
ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV
SMF - transport modelcalculations
experimental data (B Tsang et al PRL 92 (2004) )
Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and
Imbalance ratios
x = β = (N-Z)A
τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation
M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn
Kinetic energy loss
L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn
Time
JRizzo et al NPA806 (2008) 79
Several isoscalarinteractions
Unstable dynamics
Liquid-gas phase transitionFragmentation in exotic systems
Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm
Sn124 + Sn124 EA = 50 MeVA
Central collisions
Ni + Au EA = 45 MeVA
(fluctuations projected on ordinary space)
Isospin-dependent liquid-gas phase transition
Isospin distillation the liquid phase is more symmetric than the gas phase
β = 02
β = 01
Non-homogeneous density
asy-stiff - - -asy-soft
Density gradients derivative of Esym
asy-soft
asy-stiff
Spinodal decomposition in a box (quasi-analytical calculations)
β = 02
β = 01
NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo
Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606
arXiv07073416
arXiv07073416Cluster density
asy-soft
asy-stiff
Sn112 + Sn112
Sn124 + Sn124
b = 6 fm 50 AMeV
Isospin migration in neck fragmentationIsospin migration in neck fragmentation
Transfer of asymmetry from PLF and TLF to the low density neck region
Effect related to the derivative of the symmetryenergy with respect to density
PLF TLFneckemittednucleons
ρ1 lt ρ2
Asymmetry flux
asy-stiff
asy-soft
Larger derivative with asy-stiff larger isospin migration effects
Density gradients derivative of Esym
EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007
Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics
LNS data ndash CHIMERA coll
VrelVViola (IMFPLF)
(IMFTLF)
JRizzo et al NPA806 (2008) 79
Reactions at intermediate energies
Information on high density behaviorof Esym
scattering nuclear interaction from meson exchange main channels (plus correlations)
Isoscalar Isovector
Attraction amp Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ
ρψψˆ
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
21ˆˆ
41ˆˆˆ
21ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space
Esym= kin + (vector) ndash ( scalar)
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
EOS of Symmetric and Neutron MatterEOS of Symmetric and Neutron Matter
Dirac-BruecknerRMFDensity-Dependent couplings
Symmetric Matter | Symmetry Energy | Neutron Matter
DD-F
NLρ
NLρδ
Constraints from compact stars amp heavy ion dataTKlaehn et al PRC 74 (2006) 035802
Slope at normal densityIsospin transport at Fermi energies
BOB
Urbana
AFDMC
asy-soft
asy-stiff
Effective parameterizationsof symmetry energy
Transport codesNuclear Dynamics
Astrophysical problems
SGandolfi et al PRL98(2007)102503
Extracting information on the symmetry energy Extracting information on the symmetry energy from terrestrial labs from terrestrial labs
Fermi energies 10-60 MeVA (below and around normal density) GDR Charge equilibration Fragmentation in exotic systems
Intermediate energies 01-05 GeVA (above normal density) Meson production (pions kaons) Collective response (flows)
Nuclear DynamicsNuclear Dynamics
High density behavior Neutron stars
Transport equations
Phys Rep 389 (2004)
PhysRep410(2005)335
( ) ( ) ( ) ( ) ( )K r p t K r p t p p r r r t t
fWWfdtdf
Ensemble average
Langevin randomwalk in phase-space
Semi-classical approach to the many-body problemTime evolution of the one-body distribution function ( )f r p t
Boltzmann
)()()()()( tprKfKprffhprft
LangevinVlasov
Vlasov Boltzmann Langevin
)(2
)(2
fUm
pfhi
i
Vlasov mean field
Boltzmann average collision term
( ) ( ) NNf i f i
dp p E Ed
3 3 32 1 2
2 1 23 3 3( ) (12 1 2 )d p d p d pW r p f f f wh h h
Loss term
D(pprsquor)
SMF model fluctuations projected onto ordinary space density fluctuations δρ
Fluctuation variance σ2f = ltδfδfgt
D(pprsquor) w
Collective excitations
Charge equilibration
Relativistic nuclear excitation of GDRin the target in semi-peripheral collisions
Equations of motion for n and p centroids obtained from Einsteinrsquos set- Restoring force- Coulomb + nuclear excitation (Wood-Saxon)
Zrel = zn ndash zpXrel = xn - xp
T(b) attenuation factor due to depopulation of reaction channelsP(b) probability for a given reaction channel
DassoGallardoLanzaSofia NPA801(2008)129
(neutron skin)Larger amplitude due to nuclear field
one-phonon
two-phonon
212
2
1
1210 RR
ZN
ZN
AZZD
D(t) bremss dipole radiation CN stat GDRInitial Dipole
Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics
- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion
Symmetry energy below saturation
36Ar + 96Zr40Ar + 92Zr
BMartin et al PLB 664 (2008) 47
Experimental evidence of the extra-yield LNS data
Isospin gradients Pre-equilibrium dipole emission
SPIRALS rarr Collective Oscillations
22
3
2
)(3
2
DA
NZEc
edEdP
Bremsstrahlung Quantitative estimations
VBaran DMBrink MColonna MDi Toro PRL87(2001)
iDKD
pNZ
PPPtDK
xNZ
XtXtXA
NZtD
npinpnp
npinpnp
1)(
1)()()(
TDHF CSimenel PhChomaz Gde France
132Sn + 58Ni 124Sn + 58Ni
Larger restoring force with asy-soft larger strength arXiv08074118
b=8f
m
ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV
SMF - transport modelcalculations
experimental data (B Tsang et al PRL 92 (2004) )
Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and
Imbalance ratios
x = β = (N-Z)A
τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation
M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn
Kinetic energy loss
L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn
Time
JRizzo et al NPA806 (2008) 79
Several isoscalarinteractions
Unstable dynamics
Liquid-gas phase transitionFragmentation in exotic systems
Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm
Sn124 + Sn124 EA = 50 MeVA
Central collisions
Ni + Au EA = 45 MeVA
(fluctuations projected on ordinary space)
Isospin-dependent liquid-gas phase transition
Isospin distillation the liquid phase is more symmetric than the gas phase
β = 02
β = 01
Non-homogeneous density
asy-stiff - - -asy-soft
Density gradients derivative of Esym
asy-soft
asy-stiff
Spinodal decomposition in a box (quasi-analytical calculations)
β = 02
β = 01
NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo
Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606
arXiv07073416
arXiv07073416Cluster density
asy-soft
asy-stiff
Sn112 + Sn112
Sn124 + Sn124
b = 6 fm 50 AMeV
Isospin migration in neck fragmentationIsospin migration in neck fragmentation
Transfer of asymmetry from PLF and TLF to the low density neck region
Effect related to the derivative of the symmetryenergy with respect to density
PLF TLFneckemittednucleons
ρ1 lt ρ2
Asymmetry flux
asy-stiff
asy-soft
Larger derivative with asy-stiff larger isospin migration effects
Density gradients derivative of Esym
EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007
Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics
LNS data ndash CHIMERA coll
VrelVViola (IMFPLF)
(IMFTLF)
JRizzo et al NPA806 (2008) 79
Reactions at intermediate energies
Information on high density behaviorof Esym
scattering nuclear interaction from meson exchange main channels (plus correlations)
Isoscalar Isovector
Attraction amp Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ
ρψψˆ
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
21ˆˆ
41ˆˆˆ
21ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space
Esym= kin + (vector) ndash ( scalar)
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Extracting information on the symmetry energy Extracting information on the symmetry energy from terrestrial labs from terrestrial labs
Fermi energies 10-60 MeVA (below and around normal density) GDR Charge equilibration Fragmentation in exotic systems
Intermediate energies 01-05 GeVA (above normal density) Meson production (pions kaons) Collective response (flows)
Nuclear DynamicsNuclear Dynamics
High density behavior Neutron stars
Transport equations
Phys Rep 389 (2004)
PhysRep410(2005)335
( ) ( ) ( ) ( ) ( )K r p t K r p t p p r r r t t
fWWfdtdf
Ensemble average
Langevin randomwalk in phase-space
Semi-classical approach to the many-body problemTime evolution of the one-body distribution function ( )f r p t
Boltzmann
)()()()()( tprKfKprffhprft
LangevinVlasov
Vlasov Boltzmann Langevin
)(2
)(2
fUm
pfhi
i
Vlasov mean field
Boltzmann average collision term
( ) ( ) NNf i f i
dp p E Ed
3 3 32 1 2
2 1 23 3 3( ) (12 1 2 )d p d p d pW r p f f f wh h h
Loss term
D(pprsquor)
SMF model fluctuations projected onto ordinary space density fluctuations δρ
Fluctuation variance σ2f = ltδfδfgt
D(pprsquor) w
Collective excitations
Charge equilibration
Relativistic nuclear excitation of GDRin the target in semi-peripheral collisions
Equations of motion for n and p centroids obtained from Einsteinrsquos set- Restoring force- Coulomb + nuclear excitation (Wood-Saxon)
Zrel = zn ndash zpXrel = xn - xp
T(b) attenuation factor due to depopulation of reaction channelsP(b) probability for a given reaction channel
DassoGallardoLanzaSofia NPA801(2008)129
(neutron skin)Larger amplitude due to nuclear field
one-phonon
two-phonon
212
2
1
1210 RR
ZN
ZN
AZZD
D(t) bremss dipole radiation CN stat GDRInitial Dipole
Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics
- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion
Symmetry energy below saturation
36Ar + 96Zr40Ar + 92Zr
BMartin et al PLB 664 (2008) 47
Experimental evidence of the extra-yield LNS data
Isospin gradients Pre-equilibrium dipole emission
SPIRALS rarr Collective Oscillations
22
3
2
)(3
2
DA
NZEc
edEdP
Bremsstrahlung Quantitative estimations
VBaran DMBrink MColonna MDi Toro PRL87(2001)
iDKD
pNZ
PPPtDK
xNZ
XtXtXA
NZtD
npinpnp
npinpnp
1)(
1)()()(
TDHF CSimenel PhChomaz Gde France
132Sn + 58Ni 124Sn + 58Ni
Larger restoring force with asy-soft larger strength arXiv08074118
b=8f
m
ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV
SMF - transport modelcalculations
experimental data (B Tsang et al PRL 92 (2004) )
Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and
Imbalance ratios
x = β = (N-Z)A
τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation
M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn
Kinetic energy loss
L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn
Time
JRizzo et al NPA806 (2008) 79
Several isoscalarinteractions
Unstable dynamics
Liquid-gas phase transitionFragmentation in exotic systems
Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm
Sn124 + Sn124 EA = 50 MeVA
Central collisions
Ni + Au EA = 45 MeVA
(fluctuations projected on ordinary space)
Isospin-dependent liquid-gas phase transition
Isospin distillation the liquid phase is more symmetric than the gas phase
β = 02
β = 01
Non-homogeneous density
asy-stiff - - -asy-soft
Density gradients derivative of Esym
asy-soft
asy-stiff
Spinodal decomposition in a box (quasi-analytical calculations)
β = 02
β = 01
NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo
Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606
arXiv07073416
arXiv07073416Cluster density
asy-soft
asy-stiff
Sn112 + Sn112
Sn124 + Sn124
b = 6 fm 50 AMeV
Isospin migration in neck fragmentationIsospin migration in neck fragmentation
Transfer of asymmetry from PLF and TLF to the low density neck region
Effect related to the derivative of the symmetryenergy with respect to density
PLF TLFneckemittednucleons
ρ1 lt ρ2
Asymmetry flux
asy-stiff
asy-soft
Larger derivative with asy-stiff larger isospin migration effects
Density gradients derivative of Esym
EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007
Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics
LNS data ndash CHIMERA coll
VrelVViola (IMFPLF)
(IMFTLF)
JRizzo et al NPA806 (2008) 79
Reactions at intermediate energies
Information on high density behaviorof Esym
scattering nuclear interaction from meson exchange main channels (plus correlations)
Isoscalar Isovector
Attraction amp Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ
ρψψˆ
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
21ˆˆ
41ˆˆˆ
21ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space
Esym= kin + (vector) ndash ( scalar)
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
( ) ( ) ( ) ( ) ( )K r p t K r p t p p r r r t t
fWWfdtdf
Ensemble average
Langevin randomwalk in phase-space
Semi-classical approach to the many-body problemTime evolution of the one-body distribution function ( )f r p t
Boltzmann
)()()()()( tprKfKprffhprft
LangevinVlasov
Vlasov Boltzmann Langevin
)(2
)(2
fUm
pfhi
i
Vlasov mean field
Boltzmann average collision term
( ) ( ) NNf i f i
dp p E Ed
3 3 32 1 2
2 1 23 3 3( ) (12 1 2 )d p d p d pW r p f f f wh h h
Loss term
D(pprsquor)
SMF model fluctuations projected onto ordinary space density fluctuations δρ
Fluctuation variance σ2f = ltδfδfgt
D(pprsquor) w
Collective excitations
Charge equilibration
Relativistic nuclear excitation of GDRin the target in semi-peripheral collisions
Equations of motion for n and p centroids obtained from Einsteinrsquos set- Restoring force- Coulomb + nuclear excitation (Wood-Saxon)
Zrel = zn ndash zpXrel = xn - xp
T(b) attenuation factor due to depopulation of reaction channelsP(b) probability for a given reaction channel
DassoGallardoLanzaSofia NPA801(2008)129
(neutron skin)Larger amplitude due to nuclear field
one-phonon
two-phonon
212
2
1
1210 RR
ZN
ZN
AZZD
D(t) bremss dipole radiation CN stat GDRInitial Dipole
Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics
- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion
Symmetry energy below saturation
36Ar + 96Zr40Ar + 92Zr
BMartin et al PLB 664 (2008) 47
Experimental evidence of the extra-yield LNS data
Isospin gradients Pre-equilibrium dipole emission
SPIRALS rarr Collective Oscillations
22
3
2
)(3
2
DA
NZEc
edEdP
Bremsstrahlung Quantitative estimations
VBaran DMBrink MColonna MDi Toro PRL87(2001)
iDKD
pNZ
PPPtDK
xNZ
XtXtXA
NZtD
npinpnp
npinpnp
1)(
1)()()(
TDHF CSimenel PhChomaz Gde France
132Sn + 58Ni 124Sn + 58Ni
Larger restoring force with asy-soft larger strength arXiv08074118
b=8f
m
ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV
SMF - transport modelcalculations
experimental data (B Tsang et al PRL 92 (2004) )
Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and
Imbalance ratios
x = β = (N-Z)A
τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation
M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn
Kinetic energy loss
L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn
Time
JRizzo et al NPA806 (2008) 79
Several isoscalarinteractions
Unstable dynamics
Liquid-gas phase transitionFragmentation in exotic systems
Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm
Sn124 + Sn124 EA = 50 MeVA
Central collisions
Ni + Au EA = 45 MeVA
(fluctuations projected on ordinary space)
Isospin-dependent liquid-gas phase transition
Isospin distillation the liquid phase is more symmetric than the gas phase
β = 02
β = 01
Non-homogeneous density
asy-stiff - - -asy-soft
Density gradients derivative of Esym
asy-soft
asy-stiff
Spinodal decomposition in a box (quasi-analytical calculations)
β = 02
β = 01
NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo
Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606
arXiv07073416
arXiv07073416Cluster density
asy-soft
asy-stiff
Sn112 + Sn112
Sn124 + Sn124
b = 6 fm 50 AMeV
Isospin migration in neck fragmentationIsospin migration in neck fragmentation
Transfer of asymmetry from PLF and TLF to the low density neck region
Effect related to the derivative of the symmetryenergy with respect to density
PLF TLFneckemittednucleons
ρ1 lt ρ2
Asymmetry flux
asy-stiff
asy-soft
Larger derivative with asy-stiff larger isospin migration effects
Density gradients derivative of Esym
EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007
Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics
LNS data ndash CHIMERA coll
VrelVViola (IMFPLF)
(IMFTLF)
JRizzo et al NPA806 (2008) 79
Reactions at intermediate energies
Information on high density behaviorof Esym
scattering nuclear interaction from meson exchange main channels (plus correlations)
Isoscalar Isovector
Attraction amp Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ
ρψψˆ
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
21ˆˆ
41ˆˆˆ
21ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space
Esym= kin + (vector) ndash ( scalar)
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Collective excitations
Charge equilibration
Relativistic nuclear excitation of GDRin the target in semi-peripheral collisions
Equations of motion for n and p centroids obtained from Einsteinrsquos set- Restoring force- Coulomb + nuclear excitation (Wood-Saxon)
Zrel = zn ndash zpXrel = xn - xp
T(b) attenuation factor due to depopulation of reaction channelsP(b) probability for a given reaction channel
DassoGallardoLanzaSofia NPA801(2008)129
(neutron skin)Larger amplitude due to nuclear field
one-phonon
two-phonon
212
2
1
1210 RR
ZN
ZN
AZZD
D(t) bremss dipole radiation CN stat GDRInitial Dipole
Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics
- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion
Symmetry energy below saturation
36Ar + 96Zr40Ar + 92Zr
BMartin et al PLB 664 (2008) 47
Experimental evidence of the extra-yield LNS data
Isospin gradients Pre-equilibrium dipole emission
SPIRALS rarr Collective Oscillations
22
3
2
)(3
2
DA
NZEc
edEdP
Bremsstrahlung Quantitative estimations
VBaran DMBrink MColonna MDi Toro PRL87(2001)
iDKD
pNZ
PPPtDK
xNZ
XtXtXA
NZtD
npinpnp
npinpnp
1)(
1)()()(
TDHF CSimenel PhChomaz Gde France
132Sn + 58Ni 124Sn + 58Ni
Larger restoring force with asy-soft larger strength arXiv08074118
b=8f
m
ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV
SMF - transport modelcalculations
experimental data (B Tsang et al PRL 92 (2004) )
Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and
Imbalance ratios
x = β = (N-Z)A
τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation
M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn
Kinetic energy loss
L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn
Time
JRizzo et al NPA806 (2008) 79
Several isoscalarinteractions
Unstable dynamics
Liquid-gas phase transitionFragmentation in exotic systems
Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm
Sn124 + Sn124 EA = 50 MeVA
Central collisions
Ni + Au EA = 45 MeVA
(fluctuations projected on ordinary space)
Isospin-dependent liquid-gas phase transition
Isospin distillation the liquid phase is more symmetric than the gas phase
β = 02
β = 01
Non-homogeneous density
asy-stiff - - -asy-soft
Density gradients derivative of Esym
asy-soft
asy-stiff
Spinodal decomposition in a box (quasi-analytical calculations)
β = 02
β = 01
NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo
Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606
arXiv07073416
arXiv07073416Cluster density
asy-soft
asy-stiff
Sn112 + Sn112
Sn124 + Sn124
b = 6 fm 50 AMeV
Isospin migration in neck fragmentationIsospin migration in neck fragmentation
Transfer of asymmetry from PLF and TLF to the low density neck region
Effect related to the derivative of the symmetryenergy with respect to density
PLF TLFneckemittednucleons
ρ1 lt ρ2
Asymmetry flux
asy-stiff
asy-soft
Larger derivative with asy-stiff larger isospin migration effects
Density gradients derivative of Esym
EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007
Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics
LNS data ndash CHIMERA coll
VrelVViola (IMFPLF)
(IMFTLF)
JRizzo et al NPA806 (2008) 79
Reactions at intermediate energies
Information on high density behaviorof Esym
scattering nuclear interaction from meson exchange main channels (plus correlations)
Isoscalar Isovector
Attraction amp Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ
ρψψˆ
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
21ˆˆ
41ˆˆˆ
21ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space
Esym= kin + (vector) ndash ( scalar)
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Relativistic nuclear excitation of GDRin the target in semi-peripheral collisions
Equations of motion for n and p centroids obtained from Einsteinrsquos set- Restoring force- Coulomb + nuclear excitation (Wood-Saxon)
Zrel = zn ndash zpXrel = xn - xp
T(b) attenuation factor due to depopulation of reaction channelsP(b) probability for a given reaction channel
DassoGallardoLanzaSofia NPA801(2008)129
(neutron skin)Larger amplitude due to nuclear field
one-phonon
two-phonon
212
2
1
1210 RR
ZN
ZN
AZZD
D(t) bremss dipole radiation CN stat GDRInitial Dipole
Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics
- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion
Symmetry energy below saturation
36Ar + 96Zr40Ar + 92Zr
BMartin et al PLB 664 (2008) 47
Experimental evidence of the extra-yield LNS data
Isospin gradients Pre-equilibrium dipole emission
SPIRALS rarr Collective Oscillations
22
3
2
)(3
2
DA
NZEc
edEdP
Bremsstrahlung Quantitative estimations
VBaran DMBrink MColonna MDi Toro PRL87(2001)
iDKD
pNZ
PPPtDK
xNZ
XtXtXA
NZtD
npinpnp
npinpnp
1)(
1)()()(
TDHF CSimenel PhChomaz Gde France
132Sn + 58Ni 124Sn + 58Ni
Larger restoring force with asy-soft larger strength arXiv08074118
b=8f
m
ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV
SMF - transport modelcalculations
experimental data (B Tsang et al PRL 92 (2004) )
Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and
Imbalance ratios
x = β = (N-Z)A
τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation
M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn
Kinetic energy loss
L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn
Time
JRizzo et al NPA806 (2008) 79
Several isoscalarinteractions
Unstable dynamics
Liquid-gas phase transitionFragmentation in exotic systems
Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm
Sn124 + Sn124 EA = 50 MeVA
Central collisions
Ni + Au EA = 45 MeVA
(fluctuations projected on ordinary space)
Isospin-dependent liquid-gas phase transition
Isospin distillation the liquid phase is more symmetric than the gas phase
β = 02
β = 01
Non-homogeneous density
asy-stiff - - -asy-soft
Density gradients derivative of Esym
asy-soft
asy-stiff
Spinodal decomposition in a box (quasi-analytical calculations)
β = 02
β = 01
NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo
Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606
arXiv07073416
arXiv07073416Cluster density
asy-soft
asy-stiff
Sn112 + Sn112
Sn124 + Sn124
b = 6 fm 50 AMeV
Isospin migration in neck fragmentationIsospin migration in neck fragmentation
Transfer of asymmetry from PLF and TLF to the low density neck region
Effect related to the derivative of the symmetryenergy with respect to density
PLF TLFneckemittednucleons
ρ1 lt ρ2
Asymmetry flux
asy-stiff
asy-soft
Larger derivative with asy-stiff larger isospin migration effects
Density gradients derivative of Esym
EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007
Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics
LNS data ndash CHIMERA coll
VrelVViola (IMFPLF)
(IMFTLF)
JRizzo et al NPA806 (2008) 79
Reactions at intermediate energies
Information on high density behaviorof Esym
scattering nuclear interaction from meson exchange main channels (plus correlations)
Isoscalar Isovector
Attraction amp Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ
ρψψˆ
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
21ˆˆ
41ˆˆˆ
21ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space
Esym= kin + (vector) ndash ( scalar)
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
212
2
1
1210 RR
ZN
ZN
AZZD
D(t) bremss dipole radiation CN stat GDRInitial Dipole
Pre-equilibrium Dipole RadiationCharge Equilibration DynamicsStochastic rarr Diffusion vsCollective rarr Dipole Oscillations of the Di-nuclear System Fusion Dynamics
- Isovector Restoring Force- Neutron emission- Neck Dynamics (Mass Asymmetry)- Anisotropy- Cooling on the way to Fusion
Symmetry energy below saturation
36Ar + 96Zr40Ar + 92Zr
BMartin et al PLB 664 (2008) 47
Experimental evidence of the extra-yield LNS data
Isospin gradients Pre-equilibrium dipole emission
SPIRALS rarr Collective Oscillations
22
3
2
)(3
2
DA
NZEc
edEdP
Bremsstrahlung Quantitative estimations
VBaran DMBrink MColonna MDi Toro PRL87(2001)
iDKD
pNZ
PPPtDK
xNZ
XtXtXA
NZtD
npinpnp
npinpnp
1)(
1)()()(
TDHF CSimenel PhChomaz Gde France
132Sn + 58Ni 124Sn + 58Ni
Larger restoring force with asy-soft larger strength arXiv08074118
b=8f
m
ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV
SMF - transport modelcalculations
experimental data (B Tsang et al PRL 92 (2004) )
Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and
Imbalance ratios
x = β = (N-Z)A
τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation
M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn
Kinetic energy loss
L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn
Time
JRizzo et al NPA806 (2008) 79
Several isoscalarinteractions
Unstable dynamics
Liquid-gas phase transitionFragmentation in exotic systems
Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm
Sn124 + Sn124 EA = 50 MeVA
Central collisions
Ni + Au EA = 45 MeVA
(fluctuations projected on ordinary space)
Isospin-dependent liquid-gas phase transition
Isospin distillation the liquid phase is more symmetric than the gas phase
β = 02
β = 01
Non-homogeneous density
asy-stiff - - -asy-soft
Density gradients derivative of Esym
asy-soft
asy-stiff
Spinodal decomposition in a box (quasi-analytical calculations)
β = 02
β = 01
NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo
Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606
arXiv07073416
arXiv07073416Cluster density
asy-soft
asy-stiff
Sn112 + Sn112
Sn124 + Sn124
b = 6 fm 50 AMeV
Isospin migration in neck fragmentationIsospin migration in neck fragmentation
Transfer of asymmetry from PLF and TLF to the low density neck region
Effect related to the derivative of the symmetryenergy with respect to density
PLF TLFneckemittednucleons
ρ1 lt ρ2
Asymmetry flux
asy-stiff
asy-soft
Larger derivative with asy-stiff larger isospin migration effects
Density gradients derivative of Esym
EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007
Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics
LNS data ndash CHIMERA coll
VrelVViola (IMFPLF)
(IMFTLF)
JRizzo et al NPA806 (2008) 79
Reactions at intermediate energies
Information on high density behaviorof Esym
scattering nuclear interaction from meson exchange main channels (plus correlations)
Isoscalar Isovector
Attraction amp Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ
ρψψˆ
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
21ˆˆ
41ˆˆˆ
21ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space
Esym= kin + (vector) ndash ( scalar)
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Isospin gradients Pre-equilibrium dipole emission
SPIRALS rarr Collective Oscillations
22
3
2
)(3
2
DA
NZEc
edEdP
Bremsstrahlung Quantitative estimations
VBaran DMBrink MColonna MDi Toro PRL87(2001)
iDKD
pNZ
PPPtDK
xNZ
XtXtXA
NZtD
npinpnp
npinpnp
1)(
1)()()(
TDHF CSimenel PhChomaz Gde France
132Sn + 58Ni 124Sn + 58Ni
Larger restoring force with asy-soft larger strength arXiv08074118
b=8f
m
ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV
SMF - transport modelcalculations
experimental data (B Tsang et al PRL 92 (2004) )
Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and
Imbalance ratios
x = β = (N-Z)A
τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation
M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn
Kinetic energy loss
L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn
Time
JRizzo et al NPA806 (2008) 79
Several isoscalarinteractions
Unstable dynamics
Liquid-gas phase transitionFragmentation in exotic systems
Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm
Sn124 + Sn124 EA = 50 MeVA
Central collisions
Ni + Au EA = 45 MeVA
(fluctuations projected on ordinary space)
Isospin-dependent liquid-gas phase transition
Isospin distillation the liquid phase is more symmetric than the gas phase
β = 02
β = 01
Non-homogeneous density
asy-stiff - - -asy-soft
Density gradients derivative of Esym
asy-soft
asy-stiff
Spinodal decomposition in a box (quasi-analytical calculations)
β = 02
β = 01
NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo
Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606
arXiv07073416
arXiv07073416Cluster density
asy-soft
asy-stiff
Sn112 + Sn112
Sn124 + Sn124
b = 6 fm 50 AMeV
Isospin migration in neck fragmentationIsospin migration in neck fragmentation
Transfer of asymmetry from PLF and TLF to the low density neck region
Effect related to the derivative of the symmetryenergy with respect to density
PLF TLFneckemittednucleons
ρ1 lt ρ2
Asymmetry flux
asy-stiff
asy-soft
Larger derivative with asy-stiff larger isospin migration effects
Density gradients derivative of Esym
EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007
Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics
LNS data ndash CHIMERA coll
VrelVViola (IMFPLF)
(IMFTLF)
JRizzo et al NPA806 (2008) 79
Reactions at intermediate energies
Information on high density behaviorof Esym
scattering nuclear interaction from meson exchange main channels (plus correlations)
Isoscalar Isovector
Attraction amp Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ
ρψψˆ
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
21ˆˆ
41ˆˆˆ
21ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space
Esym= kin + (vector) ndash ( scalar)
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
b=8f
m
ISOSPIN DIFFUSION AT FERMI ENERGIESISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV
SMF - transport modelcalculations
experimental data (B Tsang et al PRL 92 (2004) )
Rizzo Colonna Baran Di Toro Pfabe Wolter PRC72(2005) and
Imbalance ratios
x = β = (N-Z)A
τ symmetry energy EsymSmaller R for larger Esymtcontact energy dissipation
M 124Sn + 112SnH 124Sn + 124SnL 112Sn + 112Sn
Kinetic energy loss
L 112Sn + 112Sn H 124Sn + 124Sn M 124Sn + 112Sn
Time
JRizzo et al NPA806 (2008) 79
Several isoscalarinteractions
Unstable dynamics
Liquid-gas phase transitionFragmentation in exotic systems
Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm
Sn124 + Sn124 EA = 50 MeVA
Central collisions
Ni + Au EA = 45 MeVA
(fluctuations projected on ordinary space)
Isospin-dependent liquid-gas phase transition
Isospin distillation the liquid phase is more symmetric than the gas phase
β = 02
β = 01
Non-homogeneous density
asy-stiff - - -asy-soft
Density gradients derivative of Esym
asy-soft
asy-stiff
Spinodal decomposition in a box (quasi-analytical calculations)
β = 02
β = 01
NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo
Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606
arXiv07073416
arXiv07073416Cluster density
asy-soft
asy-stiff
Sn112 + Sn112
Sn124 + Sn124
b = 6 fm 50 AMeV
Isospin migration in neck fragmentationIsospin migration in neck fragmentation
Transfer of asymmetry from PLF and TLF to the low density neck region
Effect related to the derivative of the symmetryenergy with respect to density
PLF TLFneckemittednucleons
ρ1 lt ρ2
Asymmetry flux
asy-stiff
asy-soft
Larger derivative with asy-stiff larger isospin migration effects
Density gradients derivative of Esym
EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007
Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics
LNS data ndash CHIMERA coll
VrelVViola (IMFPLF)
(IMFTLF)
JRizzo et al NPA806 (2008) 79
Reactions at intermediate energies
Information on high density behaviorof Esym
scattering nuclear interaction from meson exchange main channels (plus correlations)
Isoscalar Isovector
Attraction amp Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ
ρψψˆ
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
21ˆˆ
41ˆˆˆ
21ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space
Esym= kin + (vector) ndash ( scalar)
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Unstable dynamics
Liquid-gas phase transitionFragmentation in exotic systems
Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm
Sn124 + Sn124 EA = 50 MeVA
Central collisions
Ni + Au EA = 45 MeVA
(fluctuations projected on ordinary space)
Isospin-dependent liquid-gas phase transition
Isospin distillation the liquid phase is more symmetric than the gas phase
β = 02
β = 01
Non-homogeneous density
asy-stiff - - -asy-soft
Density gradients derivative of Esym
asy-soft
asy-stiff
Spinodal decomposition in a box (quasi-analytical calculations)
β = 02
β = 01
NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo
Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606
arXiv07073416
arXiv07073416Cluster density
asy-soft
asy-stiff
Sn112 + Sn112
Sn124 + Sn124
b = 6 fm 50 AMeV
Isospin migration in neck fragmentationIsospin migration in neck fragmentation
Transfer of asymmetry from PLF and TLF to the low density neck region
Effect related to the derivative of the symmetryenergy with respect to density
PLF TLFneckemittednucleons
ρ1 lt ρ2
Asymmetry flux
asy-stiff
asy-soft
Larger derivative with asy-stiff larger isospin migration effects
Density gradients derivative of Esym
EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007
Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics
LNS data ndash CHIMERA coll
VrelVViola (IMFPLF)
(IMFTLF)
JRizzo et al NPA806 (2008) 79
Reactions at intermediate energies
Information on high density behaviorof Esym
scattering nuclear interaction from meson exchange main channels (plus correlations)
Isoscalar Isovector
Attraction amp Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ
ρψψˆ
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
21ˆˆ
41ˆˆˆ
21ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space
Esym= kin + (vector) ndash ( scalar)
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Stochastic mean field (SMF) calculationsb = 4 fm b = 6 fm
Sn124 + Sn124 EA = 50 MeVA
Central collisions
Ni + Au EA = 45 MeVA
(fluctuations projected on ordinary space)
Isospin-dependent liquid-gas phase transition
Isospin distillation the liquid phase is more symmetric than the gas phase
β = 02
β = 01
Non-homogeneous density
asy-stiff - - -asy-soft
Density gradients derivative of Esym
asy-soft
asy-stiff
Spinodal decomposition in a box (quasi-analytical calculations)
β = 02
β = 01
NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo
Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606
arXiv07073416
arXiv07073416Cluster density
asy-soft
asy-stiff
Sn112 + Sn112
Sn124 + Sn124
b = 6 fm 50 AMeV
Isospin migration in neck fragmentationIsospin migration in neck fragmentation
Transfer of asymmetry from PLF and TLF to the low density neck region
Effect related to the derivative of the symmetryenergy with respect to density
PLF TLFneckemittednucleons
ρ1 lt ρ2
Asymmetry flux
asy-stiff
asy-soft
Larger derivative with asy-stiff larger isospin migration effects
Density gradients derivative of Esym
EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007
Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics
LNS data ndash CHIMERA coll
VrelVViola (IMFPLF)
(IMFTLF)
JRizzo et al NPA806 (2008) 79
Reactions at intermediate energies
Information on high density behaviorof Esym
scattering nuclear interaction from meson exchange main channels (plus correlations)
Isoscalar Isovector
Attraction amp Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ
ρψψˆ
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
21ˆˆ
41ˆˆˆ
21ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space
Esym= kin + (vector) ndash ( scalar)
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Isospin-dependent liquid-gas phase transition
Isospin distillation the liquid phase is more symmetric than the gas phase
β = 02
β = 01
Non-homogeneous density
asy-stiff - - -asy-soft
Density gradients derivative of Esym
asy-soft
asy-stiff
Spinodal decomposition in a box (quasi-analytical calculations)
β = 02
β = 01
NZ and variance decrease in low-density domainsIsospin ldquotuningrdquo
Correlations of NZ vs EkinColonna amp Matera PRC77 (08) 064606
arXiv07073416
arXiv07073416Cluster density
asy-soft
asy-stiff
Sn112 + Sn112
Sn124 + Sn124
b = 6 fm 50 AMeV
Isospin migration in neck fragmentationIsospin migration in neck fragmentation
Transfer of asymmetry from PLF and TLF to the low density neck region
Effect related to the derivative of the symmetryenergy with respect to density
PLF TLFneckemittednucleons
ρ1 lt ρ2
Asymmetry flux
asy-stiff
asy-soft
Larger derivative with asy-stiff larger isospin migration effects
Density gradients derivative of Esym
EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007
Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics
LNS data ndash CHIMERA coll
VrelVViola (IMFPLF)
(IMFTLF)
JRizzo et al NPA806 (2008) 79
Reactions at intermediate energies
Information on high density behaviorof Esym
scattering nuclear interaction from meson exchange main channels (plus correlations)
Isoscalar Isovector
Attraction amp Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ
ρψψˆ
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
21ˆˆ
41ˆˆˆ
21ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space
Esym= kin + (vector) ndash ( scalar)
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Sn112 + Sn112
Sn124 + Sn124
b = 6 fm 50 AMeV
Isospin migration in neck fragmentationIsospin migration in neck fragmentation
Transfer of asymmetry from PLF and TLF to the low density neck region
Effect related to the derivative of the symmetryenergy with respect to density
PLF TLFneckemittednucleons
ρ1 lt ρ2
Asymmetry flux
asy-stiff
asy-soft
Larger derivative with asy-stiff larger isospin migration effects
Density gradients derivative of Esym
EDe Filippo et al PRC71044602 (2005)EDe Filippo et al NUFRA 2007
Experimental evidence of n-enrichment of the neckCorrelations between NZand deviation from Viola systematics
LNS data ndash CHIMERA coll
VrelVViola (IMFPLF)
(IMFTLF)
JRizzo et al NPA806 (2008) 79
Reactions at intermediate energies
Information on high density behaviorof Esym
scattering nuclear interaction from meson exchange main channels (plus correlations)
Isoscalar Isovector
Attraction amp Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ
ρψψˆ
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
21ˆˆ
41ˆˆˆ
21ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space
Esym= kin + (vector) ndash ( scalar)
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Reactions at intermediate energies
Information on high density behaviorof Esym
scattering nuclear interaction from meson exchange main channels (plus correlations)
Isoscalar Isovector
Attraction amp Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ
ρψψˆ
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
21ˆˆ
41ˆˆˆ
21ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space
Esym= kin + (vector) ndash ( scalar)
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
scattering nuclear interaction from meson exchange main channels (plus correlations)
Isoscalar Isovector
Attraction amp Repulsion Saturation
OBE
JggVmW
ggΦm
ψψˆˆ
ρψψˆ
2
S2
Scalar Vector Scalar Vector
VVmWWΦmΦΦΦgMVgiL ˆˆ
21ˆˆ
41ˆˆˆ
21ˆˆ 222
Nuclear interaction by Effective Field Theoryas a covariant Density Functional Approach
Quantum Hadrodynamics (QHD) rarr Relativistic Transport Equation (RMF)
Relativistic structure alsoin isospin space
Esym= kin + (vector) ndash ( scalar)
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
RBUU transport equation
Collision term
collprr IfUfmp
tf
Wigner transform cap Dirac + Fields Equation Relativistic Vlasov Equation + Collision Termhellip
Non-relativistic Boltzmann-Nordheim-Vlasov
drift mean fieldisi
iii
Mm
kk
F
ldquoLorentz Forcerdquorarr Vector Fields mean-field + pure relativistic term
Self-Energy contributions to the inelastic channels
Vector field
Scalar field
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Au+Au central π and K yield ratios vs beam energy
Pions large effects at lower energies
Kaons~15 difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
GFerini et alPRL 97 (2006) 202301
NL
NLρ
NLρδ BF
Fsym E
MffEkE
2
2
2
21
61 2
m
gf
RMF Symmetry Energy the δ -mechanism
Effects on particle production
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Collective (elliptic) flowCollective (elliptic) flow
Out-of-plane
yyx
yxt pp
pppy 22
22
2 )(V
)(V)(V)(V n2
p2
n-p2 ttt ppp
1 lt V2 lt +1
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows
)(1)(1
)(1)(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al PRL2002
High pT selection
mnltmp larger neutron squeeze out at mid-rapidity
Measure of effective masses in high density ndash highly asymmetric matter
VGiordano Diploma Thesis
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Neutron stars as laboratories for the study of dense matter
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Facts about Neutron Stars bull M ~ 1 to 2M0 ( M0=19981033g)bull R ~ 10 Km bull N obs Pulsars - 1500bull P gt 158 ms (630 Hz)bull B = 108 divide 1013 Gaussinner core = 1fm3 dNN=1 fm
hadron-to-quark transition
Tolmann-Oppenheimer-Volkov equationConclusions1) transition to quark phase reduces the
maximum mass to values similar to data
2) results very sensitive to the confinement parameter DNeutron Star Mass-Radius DiagramNeutron Star Mass-Radius Diagram
PengLiLombardo PRC77 (08) 065807
CDDM model
)()(
()()
)()(
33
33
33
TPTP
TT
QQB
QHHB
H
QH
QQB
QB
HHB
HB
density and charge conservation
Gibbs equilibrium condition +
Density dependent quark massBonn B
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Including quarks MGM0 about 15 no metastable hybrid PNS Rather low limiting masses of PNS
NJL the onset of the pure quark phase in the inner core marks an instability No transition to quarks with hyperons smaller masses than NS no metastability masses around 18
Serious problems for our understanding of the EOS if large masses (about 2) are observed
Baryonic EOS including hyperons soft EOS MGM0 about 15 at finite Ttoo small masses for NS at T = 0 Metastability of hot PNS
Hybrid starsHybrid stars
Nicotra Baldo Burgio Schulze PRD74(06)123001Burgio amp Plumari PRD77(08)085022
2
13
2
4
)21)(41)(1(
rdrdm
rm
mrPP
rm
drdP
Tolmann-Oppenheimer-Volkov equation
Schulze et al
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
MBaldo amp C Maieron PRC 77 015801 (2008)
Inner crust of NS nuclear lattice permeated by a gas of neutronsAt a given point nuclei merge and form more complicated structures Study of EOS of pure neutron matter
QMC
EOS of low-density neutron matter EOS of low-density neutron matter
- Only s-wave matters but the ldquounitary limitrdquo is actually never reached Despite that the energy is frac12 the kinetic energyin a wide range of density (for unitary 04-042 from QMC)
- The dominant correlation comes from the Pauli operator
- Both three hole-line and single particle potential effects are smalland essentially negligible Three-body forces negligible
- Scattering length and effective range determine completely the G-matrix
- Variational calculations are slightly above BBG Good agreement with QMC
In this density range one can get the ldquoexactrdquo neutron matter EOS
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
GasLiquid
Density
Big Bang Te
mpe
ratu
re
20
200
M
eV Plasma of
Quarks and
Gluons
Collisions
HeavyIon
1 nuclei 5
Phases of Nuclear Matter
Neutron Stars
Philippe Chomaz artistic view
Isospin
Mixed PhaseIn terrestrialLabs
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
AGeVUU 1238238 fmb 7
Exotic matter over 10 fmc
In a CM cell
Mixed phase in terrestrial labs
TGaitanos RBUU calculations
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Testing deconfinement with RIBrsquos
Hadron-RMF
trans onset of the mixed phase rarr decreases with asymmetrySignatures
DragoLavagno Di Toro NPA775(2006)102-126
Trajectories of 132Sn+124Sn semicentral
QH
QB
HBB
333 )1(
)1(
NLρ
NLρδGM3
B14 =150 MeV
1 AGeV 300 AMeV
Neutron migration to the quark clusters (instead of a fast emission)
Quark-Bag model
(two flavors)
Symmetry energies
symmetricneutron
- Large variation for hadron EOS - Quark matter Fermi contribution only
Crucial role of symmetry energy in quark matter
M Di Toro
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
QGP dynamics
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
xy z
px
py
RHICS discoveriesRHICS discoveriesWe have not just a bunch of particles but a We have not just a bunch of particles but a transient state of high energy plasma with transient state of high energy plasma with
Strong collective phenomenaStrong collective phenomena (elliptic flow v2) (elliptic flow v2) in condition similar to those 10in condition similar to those 10-5-5 s after s after
the Big Bangthe Big Bang~~15 GeVfm15 GeVfm33 gtgt gtgt c c ~ ~ 350 MeV350 MeV
(according to hydrodynamical calculations)(according to hydrodynamical calculations)
But finite mean free path But finite mean free path call for a transport approachcall for a transport approach
Quark dynamics in the QGP phaseQuark dynamics in the QGP phase
- The plasma is not a so perfect fluid hellip (hydrodynamical) scaling of v2 not observed- Importance of parton coalescence
22
22
xyxy
x
22
22
2 2cosyx
yx
pppp
v
nn
TT
ndpdN
ddpdN )cos(v21
Perform a Fourier expansion of the momentum space particle distributions
Parton cascade
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Kinetic Theoryvv22εε scaling broken v2ltv2gt scaling broken v2ltv2gt scaling reproducedscaling reproducedwhat about vwhat about v22 absolute absolute valuevalue
s 01-02 + freeze-outOpen the room to need coalescence in the region of Quark Number Scaling
Finite cross section calculations corresponding to constant finite shear viscosity(quantum limit) can reproduce experimental featuresNo freeze-out
Quantum mechanism s gt 115
λ151
ps
131
T
tE
No freeze-outs=14
vv22(p(pTT) as a measure of ) as a measure of ss
Ferini et al 0805 4814 [nucl-th]
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Ab initio partonic transport code p-p collisions
hellipwith the possibility to include an LQCD inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Kinetic approach to relativistic heavy ion collisionsKinetic approach to relativistic heavy ion collisions
Total cross sectionPredictions for rapidity distributions at LHC
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Conclusions and Perspectives Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are important for the study of fundamental properties of nuclear matter The ldquoelusiverdquo symmetry energy behavior far from normal density(consensus on Esym~(ρρ0) with γ~07-1 at low density)Evidences from Giant Monopole Resonance in 112-124Sn isotopesTLi et al PRL99(2007)162503
Still large uncertainties at high density Cross-check with the predictions of BBG theory
High density behavior neutron starsneutron stars
Transition to the quark phase Role of isospin to be investigatedQuark dynamics in the QGP phase collective flows and hadronization mechanisms in UrHIC
γ
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Rotation on the Reaction Plane of the Emitting Dinuclear System
iffix
xaPaWW
)sin()cos(
43
41)(cos1)( 2220
ΔΦ=2 rarr x=0 rarr a2=-14 Statistical result Collective Prolate on the Reaction Plane
ΔΦ=0 rarr Φi =Φf = Φ0
)(cos)sin1(1)( 202
PW
No rotation Φ0=0 rarr sin2θγ pure dipole
Φi
Φf
Dynamical-dipole emission
Charge equilibrium
Beam Axis
θγ photon angle vs beam axisAverage over reaction planes
All probedRotating angles
36Ar+96Zr vs 40Ar+92Zr 16AMeV Fusion events same CN selection
Angular distribution of the extra-yield (prompt dipole) anisotropy
Accurate Angular Distrib Measure Dipole Clock
Martin et al Simulations
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s (D
R)
Central collisions
pn
r
arXiv07073416
DR = (NZ)2 (NZ)1
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Last page (252) of the review ldquoRecent Progress and New Challenges in Isospin Physics with HICrdquo Bao-An Li Lie-Wen Chen Che Ming KoArXiv08043580 22 Apr 2008 (Phys Rep 464 (2008) 113-281)
Conclusions optimistic
Chimera-LAND at GSI Samurai Int Collat RIKENExotic Beams at FAIR
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (consensus on Esym~(ρρ0) with γ~07-1 at low density)Still large uncertainty at high density
It is important to disantangle isovector from isoscalar effects Cross-check of ldquoisoscalarrdquo and ldquoisovectorrdquo observables
VBaran (NIPNE HHBucharest) MDi Toro J Rizzo (LNS-Catania)F Matera (Florence) M Zielinska-Pfabe (Smith College) HH Wolter (Munich)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132EA = 50 MeV b=2 fm
N = Σi Ni Z = Σi Zi 3le Zi le 10 asy-stiff - - -asy-soft
Protonneutron repulsionlarger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy in n-rich systems
To access the variation of NZ vs E ldquoshiftedrdquo NZ NZs = NZ ndash NZ(E=0) Larger sensitivity to the asy-EoSis observed in the double NZs ratio If NZfin = a(NZ +b) NZs not affected by secondary decay
Different radial flows for neutrons and protonsFragmenting source with isospin gradient NZ of fragments vs Ekin
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Transverse flow of light clusters 3H vs 3He
mngtmp mnltmp
129Xe+124Sn 100AMeV 124Xe+112Sn 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor mngtmp
TritonHelium transverse flow ratiosmaller for mngtmp
Good sensitivity to the mass splitting
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
dppddp )sin(Set of coordinates
)sin( p = 260 MeVc Δp = 10 MeVc
t = 0 fmc t = 100 fmc
)cos(3
23
pV
The variance of the distribution function
p = 190 MeVc Δθ = 30deg
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume p = 190 MeVc θ = 20deg120)(2 Ff E
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
DEVIATIONS FROM VIOLA SYSTEMATICS
r - ratio of the observed PLF-IMF relative velocity to the corresponding Coulomb velocityr1- the same ratio for the pair TLF-IMF
The IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124 EA = 50 MeVA b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
58Fe+58Fe vs 58Ni+58Ni b=4fm 47AMeVFreeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles asy-stiffBlack circles asy-soft
Asy-soft small isospin migration
Fe fast neutron emission
Ni fast proton emission
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Liquid phase ρ gt 15 ρ0 Neighbouring cells are connected (coalescence procedure)
Extract random A nucleons among test particle distribution Coalescence procedureCheck energy and momentum conservationABonasera et al PLB244 169 (1990)
Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy
bull Correlations are introduced in the time evolution of the one-body density ρ ρ +δρ as corrections of the mean-field trajectorybull Correlated density domains appear due to the occurrence of mean-field (spinodal) instabilities at low density
Fragmentation Mechanism spinodal decomposition
Is it possible to reconstruct fragments and calculate their properties only from f
Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model
Statistical analysis of the fragmentation path
Comparison with AMD results
ChomazColonna Randrup Phys Rep 389 (2004)BaranColonnaGreco Di Toro Phys Rep 410 335 (2005)Tabacaru et al NPA764 371 (2006)
AH Raduta Colonna Baran Di Toro PRC 74034604(2006) iPRC76 024602 (2007) Rizzo Colonna Ono PRC 76 024611 (2007)
Details of SMF model
T
ρ
liquid gas
Fragment Recognition
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Angular distributions alignment characteristics
plane is the angle projected into the reaction plane between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the ldquodynamicalrdquo (gate 2) and ldquostatisticalrdquo (gate 1) components these last are more concentrated in the reaction plane
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
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- Slide 26
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- Slide 30
- Slide 31
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- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)()(
not very sensitive to Esym 124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffTXLiu et al
PRC 2004
50 AMeV
(central coll)
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
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- Slide 28
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- Slide 31
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- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
I = Iin + c(Esym tcontact) (Iav ndash Iin) Iav = (I124 + I112)2
RP = 1 ndash c RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R
IIIII2R
Imbalance ratios
If
then
50 MeVA 35 MeVA
bull Larger isospin equilibration with MI
(larger tcontact ) bull Larger isospin equilibration with asy-soft (larger Esym)bull More dissipative dynamics at 35 MeVA
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
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- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
124Sn + 64Ni 35 AMeV ternary events
NZ vs Alignement Correlation in semi-peripheral collisions
Experiment Transp Simulations (12464)
Chimera data see EDe Filippo PRussotto NN2006 Contr Rio
Asystiff
Asysoft
VBaran Aug06
Asystiff more isospin migration to the neck fragments
Histogram no selection
EDe Filippo et al PRC71(2005)
φ
vtra
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
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- Slide 20
- Slide 21
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- Slide 23
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- Slide 25
- Slide 26
- Slide 27
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- Slide 34
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- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
Au+Au 250 AMeV b=7 fm
Z=1 dataM3 centrality6ltblt75fm
Difference of np flows
Larger effects at high momenta
Triton vs 3He Flows
pn mm
Mass splitting Transverse Flow Difference
MSURIA05 nucl-th0505013 AIP ConfProc791 (2005) 70
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
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- Slide 32
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- Slide 46
- Slide 47
- Slide 48
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