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.