1. Isospin observables Observables
Mechanisms sensitive to symmetry energy
Dilute asymmetric matter and related instabilities
New features of the liquid-gas phase transition
Fragmentation in semiperipheral reactions at the
Fermi energies and degree of equilibration
Early stage of the reaction dynamics between
neutron-rich nuclei:
pre-equilibrium emission and collective flows
  Competition between different dissipative
reaction mechanisms,
like fusion vs. deep-inelastic vs. fragmentation   
Fusion dynamics in low-energy reactions:
the role of the dynamical prompt dipole radiation
(also in DIC)
Isospin effects on energetic particle production
Observables
N/Z of fragments, Isoscaling
Isospin diffusion, Imbalance ratio
Distributions of pre-equilibrium particles:
energy, angular, time,transverse momentum,
isotopic content
Correlations among light particles and/or
fragments
Differential flows (n/p, light isobars) 
    Fusion cross section vs. deep-inelastic cross
section vs. fragmentation cross section
Measure of pre-equilibrium GDR
Isospin tracer, N/Z of IMF’s in central
relativistic collisions, ratios: p+ / p- , K+/K0

2. Isoscaling: experiments and comparison
with statistical (hybrid) models (1)
Xu et al., PRL85(2000)
Tan et al., PRC64(2001) N
Sn124-Sn112 combinations
@ 50 AMeV
Comparison with SMM-MSU
(inputs from BUU, E*=4-6 MeV)
ρn = exp(α)
Isoscaling in Lattice Gas Model:
Y.G.Ma et al., PRC69
nearly linear relation with N/Z
Shetty et al., PRC70(2004)

3. Isoscaling: experiments and comparison
with statistical (hybrid) models (2)
SMM
Hot
Cold
A, fragment mass
D.Shetty et al., nucl-ex/
Tsang et al. PRC64(2001)
γ~19 MeV (SMM-McGill, canonical)

4. Isoscaling analysis in dynamical models
Stochastic BNV calculations
T.X.Liu et al., PRC69(2004)
AMD: Ono et al., PRC68(2003)
50 AMeV
35 AMeV
Isoscaling in IQMD calculations:
W.D.Tian et al., Chin.Phys.Lett.22 (2005)

5. Extraction of symmetry energy (1)
Asy-soft
Asy-stiff
E.Geraci et al.,NPA732(2004)
A.Botvina et al., PRC65(2002):
H GeV
He GeV
Shetty et al., PRC70(2004)
Isoscaling parameters depend on N/Z of systems and
value of symmetry energy: effects in opposite directions…
In SMM-MSU Csym is fixed …
Δ(Z/A)²

6. Extraction of symmetry energy (2)
Le Fevre et al., nucl-ex/
C ,600 AMeV
Fragmentation of excited target residues
Central
collisions
18O on 60 AMeV,
Fang et al., PRC61(2000)

7. Isoscaling in Deep-Inelastic Collisions: PLF sources
R21 (N,Z) = Y2/Y1
25 AMeV
•86Kr+124Sn,112Sn
(data inside gr=6.2ο)
R21 = C exp ( α N )
•86Kr+64Ni,58Ni
(data outside gr=3.5o)
G.Souliotis et al. PRC68

8. Isoscaling Parameter α vs Charge Equilibration
• 86Kr+124Sn,112Sn
• 86Kr+64Ni,58Ni
α =0.43
α =0.27
R21 = C exp ( α N )
Cold
α = 4 Csym/T ( (Z/A)12 – (Z/A)22 )
Hot
Quasi-projectiles 1: n-poor 2:nrich
G.A. Souliotis et al., Phys. Rev. C 68, (2003)

9. 86Kr, 64Ni, 136Xe data: Isocaling parameter α vs Δ(Z/A)2:
 N/Z equilibrated !
 negligible pre-eq. !
c = 19.9 0.2
*  2.0 MeV/u
86Kr+64,58Ni
c = 16.5 0.2
*  2.4 MeV/u
64Ni+124,112Sn
64Ni+64,58Ni
64Ni+232Th,208Pb
c = 13.30.4
*  2.9 MeV/u
Quasi-projectiles :
E/A ~20-25 MeV
α = 4Csym/T ( (Z/A)12 – (Z/A)22 )
Hot c
86Kr+124Sn,112Sn
No N/Z equil.
Z=32
Z=33
Cold
136Xe+124,112Sn
136Xe+64,58Ni
136Xe+232Th,197Au
c = 13.10.6
*  2.8 MeV/u
G.Souliotis et al.

10. Variation vs excitation energy
Data :
86Kr+124,112Sn
86Kr+64,58Ni
64Ni+ Ni,Sn,Th-Pb
136Xe+Ni,Sn,Th-Au
Calculation:
Mononucleus expansion
model (L. Sobotka, J. Toke)
Csym = c T / 4
Very asy-stiff below saturation
G.Souliotis et al.

11. data QP Isospin diffusion and imbalance ratio (1)
Tsang et al., PRL92(2004)
Ni AMeV
Ni AMeV
INDRA data: Galichet at al. (2005)
data QP
Imbalance ratio exp.deduced from α

12. Isospin diffusion and imbalance ratio (2)
Stochastic BNV calculations (b=8-10 fm)
gas
P T
T P
BUU calculations (b = 6 fm)
Imbalance ratio constructed from I
Tsang et al., PRL92(2004)
Ternary events ?
Baran et al., (2005)

13. IMF properties in neutron-rich systems
@600 AMeV
M.Veselsky et al., PRC62(2000)
Breakup of projectile spectators C.Sfienti et al., nucl-ex/
From isoscaling analysis
Veselsky et al., PRC69(2004)

14. Isotopic composition of sources (vs. centrality or rapidity)
Cd AMeV (mid-rapidity source)
H.Xu et al., PRC65(2002)
Milazzo et al., NPA703(2002): Ni + AMeV !
Neck Dynamics

15. Isotopic content of pre-equilibrium emission at Fermi energies
Baran et al., NPA703(2002)
AMD: Ono et al., PRC68(2003)
35 AMeV
Sn + Sn, 50 AMeV
b = 2 fm
IQMD calculations: J-Y Liu et al., PRC70(2004)
BUU calculations

16. Correlation functions and p.e. isotopic content
L-W Chen et al., PRL90(2003)
Isospin momentum dep.: m*n>m*p
Symmetry pot. reduction at high momenta
Sn132+Sn124
Asy-stiff
Asy-soft
dN/dy
dNn/dNp
B-A Li et al., NPA735(2004)
Pt(GeV/c)

17. Gas asymmetry J.Rizzo et al., (2005) Asy-soft Asy-stiff (<0/8)
AMeV, b=2 fm
m*n>m*p
m*n<m*p
J.Rizzo et al., (2005)
Asy-soft
Asy-stiff
Asy-soft
Asy-stiff
t=60 fm/c
t=80 fm/c
t=100 fm/c

18. Pre-equilibrium dipole emission (1)
O + 4,8,14,20 AMeV
Ca + 4 AMeV
O AMeV, Simenel et al., PRL86(2001)
Baran et al., PRL87(2001)

19. Pre-equilibrium dipole emission (2)
S32 + Mo100 (6 AMeV)
S32 + Mo100 (9 AMeV)
D(t)
Dk(t)
time(fm/c)
Pre-equilibrium dipole emission (2)
@25 AMeV
M.Papa et al., PRC68(2003)
D.Pierroutsakou et al. (2005)
Cooling in
hot fusion ?

20. The isospin tracer Ru,Zr combinations |Rz| = 1 transparency
Ru AMeV
Comparison with IQMD calculations
The isospin tracer
Ru,Zr combinations
|Rz| = 1 transparency
Rz = 0 full stopping
IQMD calculations
Rami et al, PRL84(2000), Hong et al., PRC66(2002)
Q.Li and Z.Li, PRC64(2001)

21. Gaitanos et al, PLB595(2004), RBUU calculations
0.4 AGev
1.528 AGev
Hong et al., PRC66(2002)
Gaitanos et al, PLB595(2004), RBUU calculations

22. IQMD calculations: Stopping and iso-fractionation
n-p differential rapidity
distribution
information on stopping
(Imbalance ratio constructed with t/He3)
@100 AMev (right panel)
fractionation effects on top
of semi-transparency
Q.Li and Z.Li, PRC64(2001)

23. Some considerations …
Improve identification of sources: contamination from pre-equilibrium emission,… (also in dynamical calculations)
Study emission time of all products, not only of nucleons (vd. neck emission)
Check thermal equilibrium of sources (see Geraci et al.)
In hybrid calculations, the statistical model should have the same symmetry energy coefficient as the dynamical model at the moment of fragment formation
Compensative effects between variances (symmetry energy value) and iso-distillation ,Δ(Z/A)², in isoscaling parameters.
Check directly isotopic distributions.

24. Some considerations…
Isoscaling is expected on a very general basis, just assuming
that isovector fluctuations have a gaussian shape:
P(δρn – δρp) ~ exp – [(δρn – δρp)² / (σ´(ρ,T)/V)]
P(N,Z) ~ exp –{ [(N-Z) - (Nº-Zº)]² / (A σ(ρ,T)) } =
exp –{ a(N-Z)²/A - bN-cZ}
b = (4 (Zº/ Aº)² - 1) / σ ; c = (4 (Nº/ Aº)²- 1) / σ
α = 4 [ (Zº/ Aº)²1 - (Zº/ Aº)²2 ] / σ
The relation between σ and the symmetry energy coefficient
depends on the fragmentation mechanism