Isospin Dynamics at the Fermi energies: Isospin Dynamics at the Fermi energies: Transport properties of the symmetry termTransport properties of the symmetry term

HIC: probing different B regions

neutron symmetric

Sly4

a4

Mean field

Effective masses

M. Di Toro, V. Baran and M. Colonna; HIC 03

N/Z fast particles

n,p correlation functions

collective flows

Chemical potentials Isospin diffusion1

Isospin distillation Isoscaling Charge equilibration1

Neck fragmentation

...)()()(),( 42 OEEE BsymBB pn

pn

02

2

2

1

EEsym

Symmetry Energy

2

0

0

0

04 183

BsymB

sym

KLaE

0

0

2

220

00

9

33

B

B

B

symsym

symB

sym

EK

PE

L

Esy

m

M

eV)

1 2 30

Expansion around

Pressure & compressibility

Asy-st

iff

Asy-soft

Mean Field & Chemical Potentials

124Sn“asymmetry” = 0.2

symmetry part of the mean field

neutron-proton chemical potentials

neutron

neutron

proton

protonbulk

neck

A

Esympn 4

spinodal interface

SG

IIS

KM

*

SkL

aS

kLb

EF

FE

CT

I VE

MA

SS

PR

OB

LE

M

I=0.192

(124S

n asym.)

pp

pp

n

n

n

n

(fm-3)

(fm-3)

pnM

M,

*

pnM

M,

*

• Spin-orbit splitting• Collective flow

RMFT, DHF( V. Greco et al., PRC63, PRC64 (2001))Agree DBHF (F. Hofmann et al., PRC64 (2001) ) SLy (E. Chabanat et al., NPA 627 (1997))

Disagree BHF (W.Zuo, PRC60 (1999) 24605)“Old” Skyrme

Splitting sign **pn MM

RMF RMF-

Effective Mass Splitting

RMF- ),( np 3fΦMM S

X<0

Y>0

X=

1+

Fs ,

Y

=1+

Fa

attractive int.0Fnp0

0

0

,

,

PT

p

yT

y

P

X<0

In Symmetric NM

PT

p

yT

yY

PX

,

,

ISOSPIN DISTILLATION: Instability Region

0P chem

ical

A UNIQUE SPINODALINSTABILITY!

V. Baran et al.PRL 86 (2001)mech. chem.