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The National Superconducting
Cyclotron Laboratory@Michigan State University
HIC Observables to probe the ASY-EOS
Bet ty Tsang
asy-stiff
asy-soft
Tests of the ASY-EOS in 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
Experimental Observables to probe the symmetry energy
E/A(,) = E/A(,0) + 2S() ; = (n- p)/ (n+ p) = (N-Z)/A
• Low densities (<0):
– Isoscaling with statistical models
– Isospin diffusion
– n/p spectra and flows; R(n/p), R(t/3He)
– Fragment isotopic distributions, R(N/Z)
– Correlation function, C(q)
– Neutron, proton radii, E1 collective modes.
• High densities (20) (Reisdorf, Lemmon, Bickley)
– Neutron/proton, t/3He spectra and flows; C(q)
– + vs. - production, k, hyperon production.
Experimental Observables to probe the symmetry energy
E/A(,) = E/A(,0) + 2S() ; = (n- p)/ (n+ p) = (N-Z)/A
• Low densities (<0):
– Isoscaling with statistical models
– Isospin diffusion
– n/p spectra and flows; R(n/p), R(t/3He)
– Fragment isotopic distributions, R(N/Z)
– Correlation function, C(q)
– Neutron, proton radii, E1 collective modes.
• High densities (20) (Reisdorf, Lemmon, Bickley)
– Neutron/proton, t/3He spectra and flows; C(q)
– + vs. - production, k, hyperon production.
Time Dependence
--Initial compression and
energy deposition
-- Expansion
-- Cooling
-- Disassembly and freezeout
Statistical Multifragmentation Model (SMM)
Single source:
(Ao, Zo), E*, Grand Canonical Approximation
=4Csym[(Z1/A1)2- (Z2/A2)
2]/T
Tsang et al. PRC 64,054615 (2002)
chemical potentialssymmetry energy
Csym is adjusted to reproduce experimental
=4Csym[(Z1/A1)2- (Z2/A2)
2]/T
Csym closely inter-related to the binding energy
3/2AaAaB SV 3/1
)1(
A
ZZaC
A
ZACsym
2)2(
3/2AaAaB SV 3/1
)1(
A
ZZaC
A
ZACsym
2)2(
Csym is closely inter-related to the binding energy
Best fit
3/2AaAaB SV 3/1
)1(
A
ZZaC
A
ZACsym
2)2(
)( 3/2AaAa SV
symsym
Csym=22.4
)( 3/2AaAa SV
symsym
3/2AaAaB SV 3/1
)1(
A
ZZaC
A
ZACsym
2)2(
)( 3/2AaAa SV
symsym
Csym=22.4
)( 3/2AaAa SV
symsym
)/
(3/1
2
A
baa
)/
(3/1
2
A
baa
Reduction of values can be accomplished with more accurate mass formula
rather than to change Csym values obtained from fitting empirical masses!
Souza et al,
arXiv:0804,1352
Shetty et al, PRC 76, 024606 (2007)
SMM describes
finite nuclei
Eint=Esym-EKE
Questionable comparisons!
Experimental Observables to probe the symmetry energy
E/A(,) = E/A(,0) + 2S() ; = (n- p)/ (n+ p) = (N-Z)/A
• Low densities (<0):
– Isoscaling with statistical models
– Isospin diffusion
– n/p spectra and flows; R(n/p), R(t/3He)
– Fragment isotopic distributions, R(N/Z)
– 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.
stiff
soft
Isospin transportTsang et al. PRL 92, 062701(2004)
gi=2; stiff
SKM; soft
Diffusion occurs within 120 fm/c.
Observable related to of the projectile/target residue
More mixing with soft S()
large Esym at <0.
Less mixing with stiff S()
...Esym=12.7(/o)
2/3 + Sint (/o)gi
stiff
soft
Isospin transport
Diffusion occurs within 120 fm/c.
Observable related to of the projectile/target residue
More mixing with soft S()
large Esym at <0.
Less mixing with stiff S()
Esym=12.7(/o)2/3 + Sint (/o)
gi
Tsang et al. PRL 92, 062701(2004)
Constraints from Isospin Diffusion Datafrom one set of data with one set of calculation!
M.B. Tsang et. al.,PRL 92, 062701 (2004)
Constraints from Isospin Diffusion Datafrom one set of data with one set of calculation!
M.B. Tsang et. al.,PRL 92, 062701 (2004)
L.W. Chen, C.M. Ko, and B.A. Li,PRL 94, 032701 (2005)
Constraints from Isospin Diffusion Datafrom one set of data with one set of calculation!
M.B. Tsang et. al.,PRL 92, 062701 (2004)
L.W. Chen, C.M. Ko, and B.A. Li,PRL 94, 032701 (2005)
C.J. Horowitz and J. Piekarewicz,PRL 86, 5647 (2001)
B.A. Li and A.W. Steiner,nucl-th/0511064
Need more and
different data sets!
Chimera array
MSU+INFN, LNS Catania124Sn+124Sn, 124Sn+112Sn, 112Sn+124Sn, 112Sn+112Sn at E/A=35 MeV
Lower energy
Longer
interaction
times,
more N/Z
equilibrations
Reasonable agreement with ImQMD predictions
Energy loss parameter as an alternative to b?
Experimental Observables to probe the symmetry energy
• Low densities (<0):
– Isoscaling with statistical models
– Isospin diffusion
– n/p spectra and flows; R(n/p), R(t/3He)
– Fragment isotopic distributions, R(N/Z)
– 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.
E/A(,) = E/A(,0) + 2S() ; = (n- p)/ (n+ p) = (N-Z)/A
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
Double
Rat
io
Center of mass EnergyFamiano et al. RPL 97 (2006) 052701
n/p Double Ratios (central collisions)
124Sn+124Sn;Y(n)/Y(p)112Sn+112Sn;Y(n)/Y(p)
Double
Rat
io
Double Ratiominimize systematic errors
Center of mass Energy
•more accurate measurements
Tsang et al. PRL 92, 062701(2004)
Famiano et al. RPL 97 (2006) 052701
n/p Double Ratios (central collisions)
124Sn+124Sn;Y(n)/Y(p)112Sn+112Sn;Y(n)/Y(p)
Double
Rat
io
Double Ratiominimize systematic errors
Center of mass Energy
Calculations are sensitive to
models and/or model input
parameters: gi , Sint, MD
effects, NN collisions, isospin
effects in NN cross-sections,
effective n and p mass.
Famiano et al. RPL 97 (2006) 052701
Experimental Observables to probe the symmetry energy
• Low densities (<0):
– Isoscaling with statistical models
– Isospin diffusion
– n/p spectra and flows; R(n/p), R(t/3He)
– Fragment isotopic distributions, R(N/Z)
– 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.
E/A(,) = E/A(,0) + 2S() ; = (n- p)/ (n+ p) = (N-Z)/A
t/3He Double Ratios (central collisions)
124Sn+124Sn;Y(t)/Y(3He)112Sn+112Sn;Y(t)/Y(3He)
Double Ratiominimize systematic errors
Center of mass energy spectra for t and 3He
Low energy rise
comes from
Coulomb effects
not properly
taken into
account in
models.
Y(t)/Y(3He) single ratios
t/t & 3He/3He ratios to minimize Coulomb effects
ImQMD code
reproduces the overall
magnitudes of the
effects but sensitivity
to gi decreases.
Need more theoretical
study
Comparison of n/p and t/3He double ratios
At E/A=50 MeV, it is difficult to extend Y(t) and Y(3He) to
energy > 40 MeV.
Significant cluster and sequential decay effects at low energy!
Center of mass Energy
Double
Rat
io
Experimental Observables to probe the symmetry energy
• Low densities (<0):
– Isoscaling with statistical models
– Isospin diffusion
– n/p spectra and flows; R(n/p), R(t/3He)
– Fragment isotopic distributions, R(N/Z)
– 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.
E/A(,) = E/A(,0) + 2S() ; = (n- p)/ (n+ p) = (N-Z)/A
Complementary to n/p ratio info.
Effects of N/Z ratios for IMF’s (3≤ Zi ≤ 8) are small!
Differences due to sequential decays?
3≤ Zi ≤ 8
Co
lon
na et al. arX
iv:0
70
7.3
09
2
Sequential decay effects are significant
Data are more consistent with iso-stiff
3≤ Zi ≤ 8
Co
lon
na et al. arX
iv:0
70
7.3
09
2
Double ratios do not “eliminate” sequential decay effects
Sensitivity to iso-EOS is much reduced!
primary
secondary decays
data
124Sn+124Sn/112Sn+112Sn;
E/A=50 MeV
Double
Rat
io
Co
lon
na et al. arX
iv:0
70
7.3
09
2
E/A=50 MeV
Data are more consistent
with iso-stiff
New Observable : “shifted” DR KE slope of N/Z
ini
ini
Is DRs(N/Z) a robust
observable?
E/A=50 MeV
Experimental Observables to probe the symmetry energy
• Low densities (<0):
– Isoscaling with statistical models
– Isospin diffusion
– n/p spectra and flows; R(n/p), R(t/3He)
– Fragment isotopic distributions, R(N/Z)
– 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.
E/A(,) = E/A(,0) + 2S() ; = (n- p)/ (n+ p) = (N-Z)/A
Isospin effects in Two-proton sources
Central collisions Sources
p-p correlation is larger for the n-rich system
Verde et al, Preliminary
Preliminary
• Asy-soft: larger source, longer
proton emission times
• Measure at q<15 MeV/c required!
Asy-stiff
r1/2~3.6 fm
Asy-soft
r1/2~4.4 fm
r (MeV/c)
S(r
) (a
.u.)
p-p Sourcesneutron-neutron
proton-proton
proton-neutron
0.0
0.5
1.0
1.5
1
2
3
4
1
3
5
7
q (MeV/c)
1+
R(q
)
IBUU: 52Ca+48Ca E/A=80 MeV
Source shape and Asy-EOS
Verde, Preliminary
Experimental Observables to probe the symmetry energy
• Low densities (<0):
– Isoscaling with statistical models
– Isospin diffusion
– n/p spectra and flows; R(n/p), R(t/3He)
– Fragment isotopic distributions, R(N/Z)
– 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.
E/A(,) = E/A(,0) + 2S() ; = (n- p)/ (n+ p) = (N-Z)/A
Model UncertaintiesD
ouble
Rat
io
Center of mass Energy
SUMMARY I: Models should explain all experimental
observables: isospin diffusions, rapidity and impact
parameter dependence, n/p ratios, N/Z ratios etc
SUMMARY II: New data, new challenges
SUMMARY III: Alternatives to n/p ratios ?
Require theoretical
understanding of
cluster formations
and more accurate
treatment of
Coulomb !Double
Rat
io
Center of mass Energy
ini
Promising observable
N/Zs(IMF). How robust ?
SUMMARY IV : We are making progress in determining the
asy-EOS at low density both experimentally and theoretically.
Do we have enough information to assign g value?
Neutron matter EOS
?
Brown, PRL 85 (2000) 5296
Chen et al. PRC 72 (2005) 064309
Fragment observables eliminate very soft asy-EOS at low density.
Acknowledgements
Theorists: W. Friedman (Wisconsin, Madison)
P. Danielewicz (MSU), S. Das Gupta (McGill,
Canada), A. Ono (Tokohu, Japan), B.A. Li, (Texas),
L. Shi (MSU), Y.X. Zhang (China), S. Souza
(Brazil), Colonna (INFN)
Experimentalists: HiRA collaboration
Michigan State University
D. Coupland, T.X. Liu (thesis), M. Famiano (n/p
expt), W.G. Lynch, Z.Y. Sun, W.P. Tan, G. Verde,
A. Wagner, H.S. Xu,
Washington University
L.G. Sobotka, R.J. Charity
Inidiana University
R. deSouza, V. E. Viola
Danielewicz, Lacey, Lynch, Science 298,1592 (2002)
Results obtained in transport
model simulations of Au+Au
collisions to reproduce the
flow (E/A~1-8 GeV)
measurements. Transport
models include constraints in
momentum dependence of the
mean field and NN cross-
sections
Summary V: Need systematic study of transport parameters
dependence on symmetry energy to resolve the inconsistencies
between models and experimental data and to provide better
constraints on the density dependence of the symmetry energy
Impact Parameter dependence of R7 is different from 35 to 50 MeV
z (fm)
MD
Larger neck
fragments are
formed when
momentum
dependence of the
mean field is
considered.
What is the effect of
MD on isospin
diffusion?
z (fm)
MI
Effects of momentum dependence of the mean field
Coupland, 2008
xAB, AB experimental or
theoretical observable for AB
xAB= a AB+b
Ri(xAB )= Ri(AB )
Rami et al., PRL, 84, 1120 (2000)
BBAA
BBAAABiR
2/)(2
Isospin Diffusion--Isospin Transport Ratio
No isospin diffusion between
symmetric systems124
124112
112
Isospin diffusion occurs only
in asymmetric systems A+B124
112
Non-isospin diffusion effects
same for A in A+B & A+A ;same for B in B+A & B+B
Observables: AB, AB (isoscaling), ln(Y(7Li)/Y(7Be))
Ri = 1
Ri = -1
y/ybeam
BUUisoscaling
R7
R7Ri()=Ri()
z (fm)
MD
z (fm)
MI
SUMMARY IV:
Systematic study
of transport
parameters
dependence on
symmetry
energy
Coupland, 2008
Emission patterns of 7Li & 7Be from 124Sn+112Sn; E/A=50 MeV
V//
CM
0
Y(7Li) enhanced from 124Sn Y(7Be) enhanced from 112Sn
112Sn+124Sn
V//(au)
Y(7Li) enhanced from 124Sn
112Sn+124Sn
V//(au)
Y(7Be) enhanced from 112Sn
Y(7Li) enhanced from 124Sn
Ratio Y(7Li)/Y(7Be)
Mainly dominated by Coulomb
112Sn+124Sn
V//(au)
Y(7Be) enhanced from 112Sn
How to observe isospin transport ?
BBAA
BBAAABi
xx
xxxR
2
Y(7Li) enhanced from 124Sn
112Sn+124Sn
x=ln(Y(7Li)/Y(7Be)
Coulomb & other
(preequilibrium &
sequential) effects are
“cancelled”
BBAA
BBAAABi
xx
xxxR
2
Liu et al., PRC, 84, 1120 (2006)
Isospin Transport Ratio
Constraining the EOS at high
densities by laboratory collisions
• The blocking by the spectator matter provides a clock with which to measure the expansion rate.
pressure
contours
density
contours