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