Neutron Number N

Pro

ton

Nu

mb

er Z 3/2AaAaB SV 3/1

)1(

A

ZZaC

A

ZAasym

2)2(

asym=30-42 MeV for infinite NM

Inclusion of surface terms in symmetry

2

23/2 )2()(

A

ZAAaAa SV

symsym

The National Superconducting Cyclotron Laboratory

@Michigan State University

Isospin Mixing and Diffusion inHeavy Ion Collisions

Betty TsangDresden, 8/2003

Ssym(

Isospin asymmetrynpnp

Can we determine the density dependence of the symmetry energy?

• Prospects are good for improving constraints further.

• Relevant for supernovae - what about neutron stars?

What is known about the EOS of symmetric matterDanielewicz, Lacey, Lynch (2002)

The density dependence of asymmetry term is largely unconstrained.

Ssym(

Measured Isotopic yields

Isoscaling from Relative Isotope Ratios

Factorization of yields into p & n densities

Cancellation of effects from sequential feedings

Robust observables to study isospin effects

R21=Y2/ Y1

TZTN pne // Zp

Nn ^ ^

Origin of isoscaling`

Isoscaling disappears when the symmetry energy is set to zero

Provides an observable to study symmetry energy

3/2AaAaB SV 3/1

)1(

A

ZZaC

A

ZAasym

2)2(

R21(N,Z)=Y2 (N,Z)/ Y1 (N,Z)

pn ZNe Zp

Nn ^ ^

Isoscaling in Antisymmetrized

Molecular Dynamical model

A. Ono et al. (2003)

Symmetry energy from AMD

(Gogny)>(Gogny-AS)Csym(Gogny)> Csym(Gogny-AS)

Multifragmentation occurs at low density

EES_fragment

Density dependence of asymmetry energy

S()=23.4(/o)

Results are model dependent

Strong influence

of symmetry term on

isoscaling

=0.36 =2/3

Consistent with many body calculations

with nn interactions

Sensitivity to the isospin terms in the EOS

Data

Y(N,Z)R21(N,Z)

SMMBUUF1,F3 N/ZP

T Freeze-out source

Asy-stiff term agrees with data better

PRC, C64, 051901R (2001).

~2 ~0.5

New observable: isospin diffusion in peripheral collisions

• Vary isospin driving forces by changing the isospin of projectile and target.

• Examine asymmetry by measuring the scaling parameter for projectile decay.

ta rg e t

p ro je c tile

symmetric system: no diffusion

weak diffusionstrong diffusion

neutron richsystem

proton richsystem

asymmetric systems

Isoscaling of mixed systems

Experimental results

3 nucleons exchange between 112 and 124

(equilibrium=6 nucleons)

Y(N,Z) / Y112+112(N,Z)=[C·exp(N + Z)]

Experimental results

3 nucleons exchange between 112 and 124

(equilibrium=6 nucleons)

Y(N,Z) / Y112+112(N,Z)=[C·exp(N + Z)]

The neck is consistent with complete mixing.

Isospin flow from n-rich projectile (target) to n-deficient target (projectile) – dynamical flow

Isospin flow is affected by the symmetry terms of the EoS – studied with BUU model

Isospin Diffusion from BUU

Isospin Transport Ratio

112112124124

1121121241242

xx

xxxRi

x=experimental or theoretical isospin observablex=x124+124 Ri = 1.x=x112+112 Ri = -1.

Experimental: isoscaling fitting parameter ; Y21 exp(N+Z)Theoretical : )/()( ZNZN

Rami et al., PRL, 84, 1120 (2000)

BUU predictions Ssym(

Ssym((

BUU predictions

Experimental results are in better agreement with predictions using hard symmetry terms

Ssym(

Ssym((

Summary

Challenge: Can we constrain the density dependence of symmetry term?

Density dependence of symmetry energy can be examined experimentally with heavy ion collisions.

Existence of isoscaling relations Isospin fractionation: Conclusions from multi

fragmentation work are model dependent; sensitivity to S().

Isospin diffusion from projectile fragmentation data provides another promising observable to study the symmetry energy with Ri

Acknowledgements

P. Danielewicz, C.K. Gelbke, T.X. Liu, X.D. Liu, W.G. Lynch,

L.J. Shi, R. Shomin, M.B. Tsang, W.P. Tan, M.J. Van

Goethem, G. Verde, A. Wagner, H.F. Xi, H.S. Xu, Akira Ono,

Bao-An Li, B. Davin, Y. Larochelle, R.T. de Souza, R.J.

Charity, L.G. Sobotka, S.R. Souza, R. Donangelo

Bill Friedman