The National Superconducting Cyclotron Laboratory Michigan State University Betty Tsang 5th ANL/MSU/JINA /INT FRIB Workshop on Bulk Nuclear Properties Nov 19-22, 2008 MSU S(Constraints on the Density dependence of Symmetry Energy in Heavy Ion Reactions
55
Embed
The National Superconducting Cyclotron Laboratory Michigan State University Betty Tsang 5th ANL/MSU/JINA/I NT FRIB Workshop on Bulk Nuclear Properties.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
The National Superconducting Cyclotron Laboratory
Michigan State University
Betty Tsang
5th ANL/MSU/JINA/I
NT FRIB Workshop on
Bulk Nuclear Properties
Nov 19-22, 2008MSU
S(
Constraints on the Density dependence of Symmetry Energy in Heavy Ion Reactions
Extracting Density dependence of Symmetry Energy in Heavy Ion Reactions
F1
F3 Outline:
What does HIC have to offer?
What are the pitfalls (in theory)?
What constraints do we have now? (Are the constraints believable or reliable?)
What research directions are we going towards FRIB?
Extracting Density dependence of Symmetry Energy in Heavy Ion Reactions
F1
F3
HIC provides a range of density determined from incident energy and impact parameter
Micha Kilburn
Bulk nuclear matter properties from Heavy Ion Central Collisions
Highest density reached by central collisions depends on incident beam energy.
Types of particles formed depend on emission times and density.
Pions, n, p fragments
E/A=1600 MeV
200 MeV50 MeV
• Experiment: measure collective flow (emission patterns) of particles emitted in Au+Au collisions from (E/A~1-8 GeV).
• Transport model (BUU) relates the measurements to pressure and density.
Charged fragments (Z=3-20) are formed at subnormal density
II. Statistical models:Describe longer time scale decays from single source. •nuclear mass, •level densities, •decay ratesUncertaintiesSource parameters: Ao, Zo, Eo, Vo, JInformation obtained is for finite nuclei, not for infinite nuclear matter
I. Transport models:Describe dynamical evolution of the collision process•Self consistent mean field •n-n collisions, •Pauli exclusionUncertaintiesSemi-classicalApproximations needed to make computation feasible.
Classes of models used to interpret experimental results
Theory must predict how reaction evolves from initial contact to final observables
Symmetry energy included in the form of fragment masses – finite nuclei & valid for o only. EOS extrapolated using statistical model is questionable.
Symmetry energy included in the nuclear EOS for infinite nuclear matter at various density from the beginning of collision.
xAB, yAB experimental or theoretical observable for AByAB= a xAB+bRi(xAB )= Ri(yAB )
Rami et al., PRL, 84, 1120 (2000)
BBAA
BBAAABi xx
xxxR
2/)(
2
Experimental Observable : Isospin Diffusion --Isospin Transport Ratio
No isospin diffusion between symmetric systems
124124
112112
Isospin diffusion occurs only in asymmetric systems A+B
124112
Non-isospin diffusion effects same for A in A+B & A+A ;same for B in B+A & B+B
Non-isospin transport effects are “cancelled”??
Ri = 1
Ri = -1
Experimental Observable : Isospin Diffusion
Probe the symmetry energy at subsaturation densities in peripheral collisions, e.g. 124Sn + 112Sn
Isospin “diffuse” through low-density neck region
Projectile
Target
124Sn
112Sn
BBAA
BBAAABi xx
xxxR
2/)(
2
x(calc)=
soft
stiff
Symmetry energy drives system towards equilibrium.
•stiff EOS small diffusion; |Ri|>>0
•soft EOS fast equilibrium; Ri0
Constraints from Isospin Diffusion Dataof calculation!
M.B. Tsang et. al., PRL 92, 062701 (2004) L.W. Chen, … B.A. Li, PRL 94, 032701 (2005)
pBUU: S=12.7(/o)2/3 + 12.5 (/o)
stiffness
IBUU04 : S~31.6(/o)
stiffness
Observable in HIC is sensitive to dependence of Sand should provide constraints to symmetry energy
Experimental Observables: n/p yield ratios
-100
-50
0
50
100
0 0.5 1 1.5 2
Li et al., PRL 78 (1997) 1644
Vas
y (M
eV)
/ o
NeutronProton
F1=2u2/(1+u)
F2=u
F3=u
F1F2
F3
u =
stiff
soft
Uas
y (M
eV)
=0.3
•n and p potentials have opposite sign.
•n & p energy spectra depend on the symmetry energy softer density dependence emits more neutrons.
•More n’s are emitted from the n-rich system and softer iso-EOS.
•Effect is much larger than IBUU04 predictions inconsistent with conclusions from isospin diffusion data.
124Sn+124Sn;Y(n)/Y(p)112Sn+112Sn;Y(n)/Y(p)
Double Ratiominimize systematic errors
Dou
ble
Rat
io
Center of mass EnergyFamiano et al. RPL 97 (2006) 052701
Nuclear Collisions simulations with Transport Models – Nuclear EOS included from beginning of collisions
BUU models:Semiclassical solution of one-body distribution function.ProsDerivable, approximations better understood.ConsMean field no fluctuations BUU does not predict cluster formation
QMD:Molecular dynamics with Pauli blocking.ProsPredicts cluster productionConsCluster properties (masses, level densities) approximate Need sequential decay codes to de-excite the hot fragmentsCode used: ImQMD
At high incident energies, cluster production is weak the two models yield the same results.
Clusters are important in low energy collisions.
Cluster effects
Zha ng et al. P
LB
66 4 (2 008 )1 45
Cluster effects are important for low energy nucleons but cannot explain the large discrepancy between data and IBUU04 calculations
Analysis of n/p ratios with ImQMD model Esym=12.5(/o)2/3 + 17.6 (/o)
i
i
Data need better measurements but the trends and magnitudes still give meaningful 2 analysis at 2 level
Analysis of isospin diffusion data with ImQMD model
BBAA
BBAAABi xx
xxxR
2/)(
2 i
S=12.5(/o)2/3 + 17.6 (/o)
x(data)=x(QMD)=
EquilibriumRi=0
No diffusionRi =1; Ri =-1
i
Impact parameter is not well determined in the experiment
b~5.8 – 7.2 fm
Analysis of rapidity dependence of Ri with ImQMD model
BBAA
BBAAABi xx
xxxR
2/)(
2 i
S=12.5(/o)2/3 + 17.6 (/o)
x(data)=f(7Li/7Be)x(QMD)=
EquilibriumRi=0
No diffusionRi =1; Ri =-1
i
New analysis on rapidity dependence of isospin diffusion ratios – not possible with BUU type of simulations due to lack of fragments.
b~5.8 – 7.2 fm
How to connect different representations of the symmetry energy
Consistent constraints from the 2 analysis of three observables
S=12.5(/o)2/3 + 17.6 (/o)
i
i
i
i
IBUU04 : S~31.6(/o)
approximation
For the first time, we have a transport model that describes np ratios and two isospin diffusion measurements
i
Expansion around 0: slope L & curvature Ksym
...183
2
0
0
0
0
BsymB
o
KLSS
LSymmetry pressure Psym
symB
sym PE
LB
00
33
0
S=12.5(/o)2/3 + 17.6 (/o) i
IQM
D
i
ImQMD
S~31.6(/o)
IBU
U04
IBUU04
IQM
D
IBU
U04
...183
2
0
0
0
0
BsymB
o
KLSS sym
B
sym PE
LB
00
33
0
S=12.5(/o)2/3 + 17.6 (/o) i
i
ImQMD
S~31.6(/o)
IBUU04Rnp=0.04 fm
S=12.5(/o)2/3 + Cs,p(/o) i
No constraints on So
ImQMDVary Cs,p and i
2 2 analysis
...183
2
0
0
0
0
BsymB
o
KLSS sym
B
sym PE
LB
00
33
0
Esym=12.5(/o)2/3 + Cs,p(/o) i
...183
2
0
0
0
0
BsymB
osym
KLSE sym
B
sym PE
LB
00
33
0
Constraints from masses and Pygmy Dipole Resonances
Esym=12.5(/o)2/3 + Cs,p(/o) i
...183
2
0
0
0
0
BsymB
osym
KLSE sym
B
sym PE
LB
00
33
0
Constraints from masses and Pygmy Dipole Resonances
Esym=12.5(/o)2/3 + Cs,p(/o) i
...183
2
0
0
0
0
BsymB
osym
KLSE sym
B
sym PE
LB
00
33
0
Current constraints on symmetry energy from HIC
Constraints on the density dependence of symmetry energy
Au+Au
?
No constraints between 0 and 2 0
FRIB
2020? FRIB
FAIR
Outlook
Precision measurements in FRIB
MSU
FRIB
FAIR
MSU (2009-2012) : E/A<100 MeV measure isospin diffusion, fragments, residues, p,n spectra ratios and differential flow improve constraints on S(, m*, nn, pp, np at <o
NSCL Dual purpose AT-TPC: proposal to be submitted to DOE
RIBF TPC: SUMARAI magnet funded, TPC – Japan-US collaboration: proposal to be submitted to DOE.
AT-TPC: FRIB
~ 1.2 M
TPC ~ 0.78 MTravel: 0.37 M
Detectors needed:
SummaryThe density dependence of the symmetry energy is of fundamental importance to nuclear physics and neutron star physics.
Observables in HI collisions provide unique opportunities to probe the symmetry energy over a range of density especially for dense asymmetric matter
Calculations suggest a number of promising observables that can probe the density dependence of the symmetry energy.
–Isospin diffusion, isotope ratios, and n/p spectral ratios provide some constraints at 0, -- refinement in constraints foreseen in near future with improvement in calculations and experiments at MSU, GANIL & Riken
– + vs. - production, n/p, t/3He spectra and differential flows may provide constraints at 20 and above, MSU, GSI, Riken
The availability of intense fast rare isotope beams at a variety of energies at RIKEN, FRIB & FAIR allows increased precisions in probing the symmetry energy at a range of densities.
Acknowledgements
NSCL Transport simulation groupBrent Barker, Abby Bickley, Dan Coupland, Krista Cruse, Pawel
Danielewicz, Micha Kilburn, Bill Lynch, Michelle Mosby, Scott Pratt, Andrew Steiner, Josh Vredevooqd, Mike Youngs, YingXun Zhang
ExperimentersMichigan State University
T.X. Liu (thesis), W.G. Lynch, Z.Y. Sun, W.P. Tan, G. Verde, A. Wagner, H.S. Xu
L.G. Sobotka, R.J. Charity (WU)R. deSouza, V. E. Viola (IU)
M. Famiano: (Westen Michigan U)
Y.X. Zhang (ImQMD), P. Danielewicz, M. Famiano, W.A. Friedman, W.G. Lynch, L.J. Shi, Jenny Lee,
How to connect different symmetry energy representations
0
10
20
30
40
50
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Total Symmetry Energy
i=0.5
i=2.0
FSU GOLDAV18skm*NL3
Esy
m (
MeV
)
/0
Value of symmetry energy at saturation
2
0
0
0
04 183
BsymB
sym
KLaE
symB
sym PE
LB
00
33
0
Expansion around 0: Symmetry slope L & curvature Ksym
Symmetry pressure Psym
40 )( aEsym
Density region sampled depends on collision observable & beamenergy• >0 examples:– Pion energy spectra– Pion production ratios– Isotopic spectra– Isotopic flow– With NSCL beams, densitiesup to 1.70 are accessible– Beams: 50-150 MeV, 50,000pps106Sn-126Sn, 37Ca-49Ca
Riken Samurai TPC
Density region sampled depends on collision observable & beamenergy• >0 examples:– Pion energy spectra– Pion production ratios– Isotopic spectra– Isotopic flow– With NSCL beams, densitiesup to 1.70 are accessible– Beams: 50-150 MeV, 50,000pps106Sn-126Sn, 37Ca-49Ca
Riken Samurai TPC
Isospin Diffusion
D
egre
e of
Asy
mm
etry
from isoscaling from Y(7Li)/Y(7Be)
Projectile
Target
124Sn
112Sn
No diffusion
Complete mixing
n-star HI collisions
/0~ 0.1 - 10 ~ 0.1-5
ye ~0.1 ~0.38-0.5
T(MeV) ~1 ~ 4-50
Extrapolate information from limited asymmetry and temperature to neutron stars!
Laboratory experiments to study properties of neutron stars
Laboratory experiments to study properties of neutron stars
208Pb
extrapolation from 208Pb radius to n-star radius
N/Z ratios from bound fragments (Z=3-8) complementary to n/p ratios
EC.M.
P T
Esym=12.7(/o)2/3 + 19(/o)i
Effects are small
Hot fragments produced in calculations.
P T
Sequential decay effects are important
Data consistent with soft EOS
N/Z ratios from bound fragments (Z=3-8) complementary to n/p ratios
Esym=12.7(/o)2/3 + 19(/o)i
Experimental Observables to probe the symmetry energy
• Symmetric Collisions 124Sn+124Sn, 112Sn+112Sn -- no diffusion
• Relative change between target and projectile is the diffusion effect
Projectile
Target
Density region sampled depends on collision observable & beamenergy• >0 examples:– Pion energy spectra– Pion production ratios– Isotopic spectra– Isotopic flow– With NSCL beams, densitiesup to 1.70 are accessible– Beams: 50-150 MeV, 50,000pps106Sn-126Sn, 37Ca-49Ca
• The density dependence of symmetry energy is largely unconstrained.
• Pressure, i.e. EOS is rather uncertain even at 0.
• The density dependence of symmetry energy is largely unconstrained.
• Pressure, i.e. EOS is rather uncertain even at 0.
Isospin Dependence of the Nuclear Equation of State