Post on 20-Dec-2015
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.
pressure contours
density contours
Danielewicz, Lacey, Lynch, Science 298,1592 (2002)
E/A(,) = E/A(,0) + 2S() ; = (n- p)/ (n+ p) = (N-Z)/AE/A(,) = E/A(,0) + 2S() ; = (n- p)/ (n+ p) = (N-Z)/A
Equation of State of Nuclear Matter
1
10
100
1 1.5 2 2.5 3 3.5 4 4.5 5
symmetric matter
RMF:NL3AkmalFermi gasFlow Exp.
P (
MeV
/fm
-3)
/0
Danielewicz, Lacey, Lynch, Science 298,1592 (2002)
Pre
ssur
e (M
eV/f
m3 )
1
10
100
1 1.5 2 2.5 3 3.5 4 4.5 5
symmetric matter
RMF:NL3AkmalFermi gasFlow ExperimentKaons ExperimentFSU Au
P (
MeV
/fm
-3)
/0
Danielewicz, Lacey, Lynch, Science 298,1592 (2002)
Pre
ssur
e (M
eV/f
m3 )
•Newer calculation and experiment are consistent with the constraints.
E/A(,) = E/A(,0) + 2S() ; = (n- p)/ (n+ p) = (N-Z)/AE/A(,) = E/A(,0) + 2S() ; = (n- p)/ (n+ p) = (N-Z)/A
Equation of State of Nuclear Matter
??
•Transport model includes constraints in momentum dependence of the mean field and NN cross-sections
Experimental Techniques to probe the symmetry energy with heavy ion collisions at E/A<100 MeV
• Vary the N/Z compositions of projectile and targets
124Sn+124Sn, 124Sn+112Sn, 112Sn+124Sn, 112Sn+112Sn
• Measure N/Z compositions of emitted particles
n & p isotopes + & - at higher incident
energyNeutron Number N
Pro
ton
Nu
mb
er Z
3/2AaAaB SV 3/1
)1(
A
ZZaC
A
ZAasym
2)2(
Isospin degree of freedom
Hub
ble
S
TCrab Pulsar
Around incident energy: E/A<100 MeV:
Reaction mechanism depends on impact parameters
Heavy Ion collision: 124Sn+124Sn, E/A=50 MeV
Neck fragmentsb=7 fm
multifragmentationb=0 fm
i=0.
5
i=2.
0
Esym=12.7(/o)2/3 + 19(/o)i
subnormal density
n & p are emitted throughout
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.
ImQMD
Y(n
)/Y
(p)
S=12.7(/o)2/3 + 17.6(/o)i
n/p Double Ratios (central collisions) 124Sn+124Sn;Y(n)/Y(p)112Sn+112Sn;Y(n)/Y(p)
Double Ratiominimize systematic errors
Data : Famiano et al. PRL 97 (2006) 052701
Will repeat experiment for better accuracy
n/p Double Ratios (central collisions)
•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
MSU (~2013) : E/A>120 MeV measure +, - spectra ratios constraints at o< <1.7o -- Bickley
Outlook
?MSU
GSI
FRIB
FAIR
GSI (2011) : E/A~400 – 800 MeV measure p,n spectra ratios and differential flow determine constraints S(, m*, nn, pp, np at 2.5o< <3o
Lemmon, Russotto et al, experimental proposal to GSI PAC
Outlook
?MSU
Riken
GSI
FRIB
FAIR
Riken (2013-2017) : E/A=200-300 MeV measure +, - spectra ratios, p,n, t/3He spectra ratios and differential flow determine S(), m*, nn, pp, np at ~2o
Riken (2011) : E/A>50 MeV measure isospin diffusions for fragments and residues determine S() at <2o.
108Sn+112,124Sn – RI beam used to increase .
Outlook
n detectors: NSCL/pre-FRIB; GSI; RIBF/Riken Pions/kaons & p, t, 3He detectors: TPC
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
E/A(,) = E/A(,0) + 2S() ; = (n- p)/ (n+ p) = (N-Z)/AE/A(,) = E/A(,0) + 2S() ; = (n- p)/ (n+ p) = (N-Z)/A
• Collision systems: 124Sn+124Sn, 124Sn+112Sn, 112Sn+124Sn, 112Sn+112Sn• E/A=50 MeV• Low densities (<0):
– n/p spectra and flows; Y(n)/Y(p), Y(t)/Y(3He), – Fragment isotopic distributions,
• Isoscaling: interpretation with statistical model is incorrect• <N>/<Z> of Z=3-8 fragments• Isospin diffusion
– Correlation function, C(q)– Neutron, proton radii, E1 collective modes.
• High densities (20) – Neutron/proton spectra and flows; C(q) + vs. - production, k, hyperon production.
asy-stiff
asy-soft
Exploring Bulk properties of Nuclear Matter with Heavy Ion Collisions
High density/energy
• differential flow
• n/p, LIF ratios
• pions ratios
• kaon ratios
• neutron stars
Low density/energy
• fragments, ratios
• isospin diffusion
• isoscaling
• migration/fractionat.
• collective excitations
• surface phenomena
• phase transitions
QF Li, Di Toro
Di Toro, Lukasic
DiToro, Reisdorf, QF Li
Prassa, QF Li
BA Li, Kubis
Tsang, HW
BA Li, HW
Tsang
Di Toro
Aumann, Ducoin
Lehaut
Danielewicz
Hermann Wolter
Constraints from Isospin Diffusion Data
124Sn+112Sn data
Data:
•Collisions of Sn+Sn isotopes at E/A=50 MeV
•b/bmax>0.8 <b>~7.2 fm from multiplicity gates.
•y/yb>0.7
•Results obtained with clusters
IBUU04:
Collisions of Sn+Sn isotopes at E/A=50 MeV
b=6 fm
Projectile-like residue determined from density &
y/yb>0.5
No clusters
x=0
x=1(soft)
x=-1
x=-2
Isospin diffusion in the projectile-like region
Basic ideas:• Peripheral reactions• Asymmetric collisions
124Sn+112Sn, 112Sn+124Sn -- diffusion
• 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
E/A (,) = E/A (,0) + 2S()
= (n- p)/ (n+ p) = (N-Z)/A
-20
-10
0
10
20
30
0 0.1 0.2 0.3 0.4 0.5 0.6
EOS for Asymmetric Matter
Soft (=0, K=200 MeV)asy-soft, =1/3 (Colonna)asy-stiff, =1/3 (PAL)
E/A
(M
eV)
(fm-3)
=(n-
p)/(
n+
p)
PAL: Prakash et al., PRL 61, (1988) 2518.Colonna et al., Phys. Rev. C57, (1998) 1410.
Brown, Phys. Rev. Lett. 85, 5296 (2001)
a/s
2 A/EP
Neutron matter EOS
dailygalaxy.com
• <0 – created in multifragmentation processObservables:– n/p ratios– Isotopic spectra– Beams: 50 MeV, 112Sn-124Sn
Transport description of heavy ion collisions:
,fIfUfm
p
t
fcollp
2-body hard collisions
)1)(1()1)(1(
)()2(
1
432432
43213412
124322
3
ffffffff
ppppd
dvdpdpdp
loss term gain term
11 1
12
3 4
non-relativistic: BUU
effective mass
Kinetic momentum
Field tensor
Relativistic BUU
),( fI coll
Vlasov eq.; mean field
EOS
Simulation with Test Particles:
me
an
px(
y0)
[M
eV
]
Analysis of rapidity dependence of Ri with ImQMD model Esym=12.5(/o)2/3 + 17.6 (/o)
i
New analysis on rapidity dependence of isospin diffusion ratios – not possible with BUU type of simulations due to lack of fragments.
i