Zbigniew Chajęcki National Superconducting Cyclotron Laboratory Michigan State University B. Lynch, B. Tsang, M. Kilburn, D. Coupland, M. Youngs Probing the symmetry energy Probing the symmetry energy with heavy ions with heavy ions
Dec 21, 2015
Zbigniew Chajęcki
National Superconducting Cyclotron Laboratory
Michigan State University
B. Lynch, B. Tsang, M. Kilburn, D. Coupland, M.
Youngs
Probing the symmetry Probing the symmetry energyenergy
with heavy ionswith heavy ions
Z. Ch. - WWND 2011, Feb 6-13, 2011 2
OutlineOutline
Symmetry energy
Probing Symmetry Energy with heavy ions
n/p , t/3He spectrum
isospin diffusion
correlations
neutron and proton emission time and symmetry energy (particle emission chronology)
pion production
Summary
Z. Ch. - WWND 2011, Feb 6-13, 2011 3
E/A (,) = E/A (,0) + 2S()
= (n- p)/ (n+ p) = (N-Z)/A
Nuclear Equation of StateNuclear Equation of State
Examples of possible research areas in NSCL/FRIB
Astrophysics Nuclear structure Nuclear reactions mass and size of neutron stars nature of neutron stars and dense nuclear matter origin of elements heavier than iron in the cosmosnuclear reactions that drive stars and stellar explosions?
Neutron skin thickness GMR PDR Isobaric Analog States nature of the nuclear
force that binds protons and neutrons into stable nuclei and rare isotopes
etc...
n/p ratios t/³He ratios Isospin diffusion Isoscalingproton-proton correlations etc...
Z. Ch. - WWND 2011, Feb 6-13, 2011 4
EOS: symmetric matter and neutron EOS: symmetric matter and neutron mattermatter
Brown, Phys. Rev. Lett. 85, 5296 (2001)
Neutron matter EOS
The density dependence of symmetry energy is largely unconstrained.
E/A (,) = E/A (,0) + 2S()
= (n- p)/ (n+ p) = (N-Z)/A
1
E/A
[MeV
]
Crucial to obtain
stellar radii
moments of interia
maximum masses
neutron star cooling rates
crustal vibration frequencies
stiff
soft
Z. Ch. - WWND 2011, Feb 6-13, 2011 5
Probes of the symmetry Probes of the symmetry energyenergy
• To maximize sensitivity, reduce systematic errors:– Vary isospin of detected particle– Vary isospin asymmetry
=(N-Z)/A of reaction.• Low densities (<0):
– Neutron/proton spectra and flows– Isospin diffusion– Correlations
• High densities (20) :– Neutron/proton spectra and flows + vs. - production– Correlations
symmetry energy
<0>0
E/A (,) = E/A (,0) + 2S() = (n- p)/ (n+ p) = (N-Z)/A
S() = 12.5·(ρ/ρ0)2/3 + Sint· (ρ/ρ0)
stiff
soft
Z. Ch. - WWND 2011, Feb 6-13, 2011 6
InternationaInternational l
CollaboratioCollaborationn
RIBFFRIB
MSU
GSI
FAIR
?
Facility Probe Beam En. [MeV]
Year Density
MSU n,p,t,3He 50-140 2009 < 0
GSI n,p,t,3He 400 2010/2011 2.5 0
MSU iso-diffusion 50 2010/2011 < 0
RIKEN iso-diffusion 50 2010 < 0
MSU 140 2012-2014 1-1.5 0
RIKEN n,p,t,3He,
200-300 2014 2 0
GSI n,p,t,3He 800 2014 2-3 0
FRIB n,p,t,3He,
200 2018- 2-2.5 0
FAIR K+,K- 800-1000 2018 3 0
E/A (,) = E/A (,0) + 2S()
= (n- p)/ (n+ p) = (N-Z)/A
Symmetry Energy Project Symmetry Energy Project CollaborationCollaboration
Determination of the Equation of State of Asymmetric Nuclear Matter NSCL MSU, USA: B. Tsang & W. Lynch, Gary Westfall, Pawel Danielewicz, Edward Brown, Andrew Steiner Rutgers University: Jolie Cizewski Smith College : Malgorzata Pfabe University of Texas, El Paso: Jorge Lopez Texas A&M University : Sherry Yennello Western Michigan University : Michael Famiano RIKEN, JP: Hiroshi Sakurai, Shunji Nishimura, Yoichi Nakai, Atsushi Taketani Kyoto University: Tetsuya MurakamiRikkyo University, JP: Jiro Murata, Kazuo Ieki Tohoku University: Akira Ono GSI DE: Wolfgang Trautmann, Yvonne Leifels, Marcus Bleicher Daresbury Laboratory, UK: Roy Lemmon INFN LNS Catania, IT: Giuseppe Verde, Angelo Pagano, Paulo Russotto, Massimo di Toro, Maria Colonna, Aldo Bonasera, Vincenzo Greco SUBATECH FR: Christoph Hartnack GANIL FR: Abdou Chbihi, John Frankland, Jean-Pierre Wieleczko Ruđer Boskovic Institute, Zoran Basrak, China Institute of Atomic Energy: Yingxun Zhang, Zhuxia Li Brazil: Sergio Souza, Raul Donangelo, Brett Carlson
Z. Ch. - WWND 2011, Feb 6-13, 2011 7
Modeling heavy-ion collisions : transport Modeling heavy-ion collisions : transport modelsmodels
• Parameter space
• not only about the symmetry energy
• also important to understand e.g. an effect of cross section (free x-section, in-medium x-section), reduced mass
• Production of clusters: d,t, 3He (alphas)
QuickTime™ and a decompressor
are needed to see this picture.
• BUU - Boltzmann-Uehling-Uhlenbeck
• Simulates two nuclei colliding
Danielewicz, Bertsch, NPA533 (1991) 712 B. A. Li et al., PRL 78 (1997) 1644
Micha Kilburn
Z. Ch. - WWND 2011, Feb 6-13, 2011 8
Probing Symmetry Energy:Probing Symmetry Energy:
Experimental ObservablesExperimental Observables
Z. Ch. - WWND 2011, Feb 6-13, 2011 9
n/p yield ratios
-100
-50
0
50
100
0 0.5 1 1.5 2
Li et al., PRL 78 (1997) 1644
Vasy
(MeV)
/ο
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 and p energy spectra depend on the symmetry energy and softer density dependence emits more neutrons at low density
•More n’s are emitted from the n-rich system and softer iso-EOS
ImQMD
Y(n
)/Y
(p)
S()=12.5(/o)2/3 +17.6(/o)i
soft
stiff
soft
stiff
Z. Ch. - WWND 2011, Feb 6-13, 2011 10
t/3He yield ratiosL-W Chen et al., PRC 69 (2004) 054606
t/3He ratio sensitive to the symmetry energy (similarly as n/p)
- advantage: easier to measure
However, the magnitude of the ratio depends also on the details within the symmetry energy potential
Z. Ch. - WWND 2011, Feb 6-13, 2011 11
Probing Symmetry Energy with n’s and p’sProbing Symmetry Energy with n’s and p’s
Density dependence of the symmetry energy with emitted neutrons and protons& Investigation of transport model parameters.
Proj Target E/A Range
40Ca 124Sn 140
> 0
40Ca 112Sn 140
48Ca 124Sn 140
48Ca 112Sn 140
124Sn 124Sn 50, 120 < 0
> 0
112Sn 112Sn 50, 120
Famiano, Coupland, Youngs
NSCL experiments 05049 & 09042NSCL experiments 05049 & 09042
Z. Ch. - WWND 2011, Feb 6-13, 2011 12
Measurement of n/p spectral ratios: probes the Measurement of n/p spectral ratios: probes the pressure due to asymmetry term at pressure due to asymmetry term at 00..
• Probe expulsion of neutrons from bound neutron-rich system by symmetry energy.
• Has been probed by direct measurements of neutrons vs. proton emission rates in central Sn+Sn collisions.
Esym=12.7(/o)2/3 + 19(/o)i
minimize systematic errors
124Sn+124Sn;Y(n)/Y(p)112Sn+112Sn;Y(n)/Y(p)
Double Ratios
•Double ratio removes the sensitivity to neutron efficiency and energy calibration.
soft
stiff
Z. Ch. - WWND 2011, Feb 6-13, 2011 13
Isospin diffusion is measured with fragments emitted from the neck region. Probe the symmetry energy at subsaturation densities in semi-peripheral
collisions, e.g. 124Sn + 112Sn at b=6 fm Isospin “diffuse” through low-density neck region
Symmetry energy drives system towards equilibrium.
=(N-Z)/A
• stiff EOS small diffusion; |Ri|>>0
• soft EOS fast equilibrium; Ri0
Projectile
Target
124Sn
112Sn
soft
stiff
Experimental Experimental observable: observable:
Isospin dependenceIsospin dependence
Ri ( ) =2⋅ −(bothn-rich +bothp-rich) / 2
bothn-rich −bothp-rich
Z. Ch. - WWND 2011, Feb 6-13, 2011 14
Isospin diffusion is measured with fragments emitted from the neck region.
Probe the symmetry energy at subsaturation densities in semi-peripheral collisions, e.g. 124Sn + 112Sn at b=6 fm
Isospin “diffuse” through low-density neck region
Symmetry energy drives system towards equilibrium.
• stiff EOS small diffusion; |Ri|>>0
• soft EOS fast equilibrium; Ri0
Experimental observable: Isospin Experimental observable: Isospin dependencedependence
Projectile Target E/A lab range
124,118,112Sn 124,118,112Sn 50 NSCL < 0124,112,108Sn 124,112Sn 50 RIKEN
S() = 12.5·(ρ/ρ0)2/3 + Sint· (ρ/ρ0)
Ri (X) =2⋅X−(XA+A + XB+B) / 2
XA+A −XB+B
X =lnY( 7Li)Y( 7Be)
⎛
⎝⎜⎞
⎠⎟
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Emission of p’s and n’s: Sensitivity to Emission of p’s and n’s: Sensitivity to SymEnSymEn
Stiff EoS Soft
EoS
Stiff EoS (γ=2)
p’s emitted after n’s
later emission times
p’s and n’s emitted at similar time
faster emission times
Soft EoS (γ=0.5)
L-W
Chen e
t al., PR
L90
(2
00
3)
16
27
01
52Ca 48Ca
Z. Ch. - WWND 2011, Feb 6-13, 2011 16
Sym.En. and correlationsSym.En. and correlations
Stiff EoS
Soft EoS
L-W
Chen e
t al., PR
L90
(2
00
3)
16
27
01
Stiff
Stiff EoS
Soft
Soft EoS
n-n, p-p, n-p correlations sensitive to the symmetry energy
Z. Ch. - WWND 2011, Feb 6-13, 2011 17
proton-proton correlationsproton-proton correlations
few fm
x1
x2
p1
p2
€
C(p1, p2 ) =P(p1, p2 )
P(p1)P(p2 )=
real event pairs
mixed event pairs
Experimental correlation function:
P(p1) - single particle distribution
P(p1, p2 ) - two particle distribution
r
|q| = 0.5 |p1 - p2|
(p,p) correlation functionP(p1,p2)
P(p1)P(p2)
|q| = 0.5 |p1 - p2|
( ) ( ) ( )rSrrdq q
rrrr
23C ∫ Φ=
( )rqr
rΦ
( )rS r… 2-particle wave function
… source function
Theoretical CF: Koonin-Pratt equationS.E. Koonin, PLB70 (1977) 43S.Pratt et al., PRC42 (1990) 2646
|q| = 0.5 |p1 - p2|
(p,p) correlation function
uncorrelated
Coulomb
S-wave interraction
Z. Ch. - WWND 2011, Feb 6-13, 2011 18
NSCL experiments 05045: HiRA + 4NSCL experiments 05045: HiRA + 4 detectordetector November 2006November 2006
- 4π detector => impact parameter + reaction plane
- HiRA => light charge particle correlations (angular coverage 20-60º in LAB,
-63 cm from target (= ball center))
beam
= High Resolution Array
Reaction systems:
40Ca + 40Ca @ 80 MeV/u
48Ca + 48Ca @ 80 MeV/u
Z. Ch. - WWND 2011, Feb 6-13, 2011 19
32 strips v. (front)
Beam
Si-E 65 m
32 strips v.(front)
Si-E 1.5 mm
pixel
32 strips h. (back)
4x CsI(Tl) 4cm
• up to 20 Telescopes • 62.3 x 62.3 mm2 active area• strip pitch 2 mm• 1024 Pixels per telescope
@ 63 cm from target => Δθ<0.2º
•ASIC readout
Telescope
Z. Ch. - WWND 2011, Feb 6-13, 2011 20
Detector performanceDetector performance
good PIDHigh resolution at low relative momentum
Z. Ch. - WWND 2011, Feb 6-13, 2011 21
Initial size effectInitial size effect
R=r0 A1/3
R(40Ca) = 4.3 fm
R(48Ca) = 4.6 fm
R 48Ca+ 48Ca > R 40Ca+ 40Ca
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Comparing data to pBUU Comparing data to pBUU
BUU PararametersNo dependence on symmetry
energyRostock in-medium reductionProducing clusters
BUU does reasonably wellExcept at forward angles -
Spectator sourceWhere evaporation and
secondary decays are important!
Forward angle
Backward angle
Micha Kilburn
Z. Ch. - WWND 2011, Feb 6-13, 2011 23
Emission of p’s and n’s: Sensitivity to Emission of p’s and n’s: Sensitivity to SymEnSymEn
Stiff EoS Soft
EoS
Stiff EoS (γ=2)
p’s emitted after n’s
later emission times
p’s and n’s emitted at similar time
faster emission times
Soft EoS (γ=0.5)
L-W
Chen e
t al., PR
L90
(2
00
3)
16
27
01
52Ca 48Ca
Z. Ch. - WWND 2011, Feb 6-13, 2011 24
n-p correlation functionn-p correlation function
few fm
x1
x2
p1
p2
( ) ( ) ( )rSrrdq q
rrrr
23C ∫ Φ=
( )rqr
rΦ
( )rS r… 2-particle wave function
… source function
Theoretical CF: Koonin-Pratt equationS.E. Koonin, PLB70 (1977) 43S.Pratt et al., PRC42 (1990) 2646
r
0 x
S(x)
(n,p) correlation function
0 x
S(x)
(n,p) correlation function
q = 0.5(p1 - p2)
Z. Ch. - WWND 2011, Feb 6-13, 2011 25
Emission of p’s and n’s: Sensitivity to Emission of p’s and n’s: Sensitivity to SymEnSymEn
Stiff EoS Soft
EoS
Stiff EoS (γ=2)
p’s emitted after n’s
later emission times
p’s and n’s emitted at similar time
faster emission times
Soft EoS (γ=0.5)
L-W
Chen e
t al., PR
L90
(2
00
3)
16
27
01
52Ca 48Ca
Z. Ch. - WWND 2011, Feb 6-13, 2011 26
Possible emission configurations (stiff Possible emission configurations (stiff sym. pot.)sym. pot.)
nCatching up
p
np
np
Catching up
Moving awayMoving away
np
0 x
S(x)
(n,p) correlation function
q = 0.5(pp - pn)
qx<0
qx<0
qx>0( ) ( ) ( )rSrrdq q
rrrr
23C ∫ Φ=
q=pp -pn =(qx, qy=0, qz=0); r =(x, y=0,z=0)
qx<0
qx>0
qx>0
Z. Ch. - WWND 2011, Feb 6-13, 2011 27
Emission of p’s and n’s: Sensitivity to Emission of p’s and n’s: Sensitivity to SymEnSymEn
Stiff EoS Soft
EoS
Stiff EoS (γ=2)
p’s emitted after n’s
later emission times
p’s and n’s emitted at similar time
faster emission times
Soft EoS (γ=0.5)
L-W
Chen e
t al., PR
L90
(2
00
3)
16
27
01
52Ca 48Ca
Z. Ch. - WWND 2011, Feb 6-13, 2011 28
Sensitivity to particle emission (soft Sensitivity to particle emission (soft sym. pot.)sym. pot.)
np
np
Catching upMoving away
0
x
S(x)
(n,p) correlation function
qx = 0.5(px,p - px,n)
qx<0 qx>0
qx<0
qx>0
( ) ( ) ( )rSrrdq q
rrrr
23C ∫ Φ=Experimentally, we measure the CF, not the source distribution!
€
C(p1, p2 ) =P(p1, p2 )
P(p1)P(p2 )=
real event pairs
mixed event pairs
P(p1) - single particle distribution
P(p1, p2 ) - two particle distribution
q=pp -pn =(qx, qy=0, qz=0); r =(x, y=0,z=0)
Z. Ch. - WWND 2011, Feb 6-13, 2011 29
Not expected if n,p emitted from the same source (no n-p differential flow)
Relating asymmetry in the CF to space-time Relating asymmetry in the CF to space-time asymmetryasymmetry
x t( ) = xp −xn( )−V tp −tn( )
(n,p) correlation function
qx = 0.5(px,p - px,n)
qx<0
qx>0
C qx( ) = dxΦ r
q x( )∫2S x t( )( )
x < 0ifx p < x n
tp > tn
⎛
⎝
⎜⎜ Protons emitted later
0x
S(x)
<x>
=0
Stiff EoS Soft
EoS
Clasically, average separation b/t protons and neutrons
Z. Ch. - WWND 2011, Feb 6-13, 2011 30
High density probe: pion High density probe: pion productionproduction
• Double ratio involves comparison between neutron rich 132Sn+124Sn and neutron deficient 112Sn+112Sn reactions.
• Double ratio maximizes sensitivity to asymmetry term.– Largely removes sensitivity
to difference between - and + acceptances.
R− / 132Sn+124 Sn( ) / 112Sn+112 Sn( )
=Y −( )
132+124/Y +( )
132+124⎡⎣
⎤⎦
Y −( )112+112
/Y +( )112+112
⎡⎣
⎤⎦
Yong et al., Phys. Rev. C 73, 034603 (2006)
soft
stiff
Facility Probe Beam En. [MeV]
Year Density
MSU 140 2012-2014 1-1.5 0
Z. Ch. - WWND 2011, Feb 6-13, 2011 31
The 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 wide 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.
Need more guidance from theory regarding observables beyond normal nuclear matter density
The availability of intense fast rare isotope beams at a variety of energies at FRIB & FAIR allows increased precisions in probing the symmetry energy at a wide range of densities
– Experimental programs are being developed to do such measurements at MSU/FRIB, RIKEN/RIBF and GSI/FAIR
SummarySummary
Z. Ch. - WWND 2011, Feb 6-13, 2011 32
Acknowledgments
• Brent Barker, Dan Brown, Zbigniew Chajecki, Dan Coupland, Pawel Danielewicz, Vlad Henzl, Daniela Henzlova, Clemens Herlitzius,
Micha Kilburn, Jenny Lee, Sergei Lukyanov, Bill Lynch, Andy Rogers, Alisher Sanetullaev, Zhiyu Sun, Betty Tsang, Andrew
Vander Molen, Gary Westfall, Mike Youngs
• NSCL-MSU
Abdou Chbihi GANIL, Caen, France
Mike Famiano Western Michigan University, Kalamazoo
Giuseppe Verde INFN, Catania, Italy
Mark Wallace LANL
Washington University, St. Louis
Romualdo DesouzaSylvie Hudan Indiana University, Bloomington
Bob CharityJon ElsonLee Sobotka