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Isospin Dynamics in Dissipative Heavy Ion Collisions
Charge Equilibration Dynamics:
The Dynamical Dipole
Competition of Dissipative Reaction
Mechanisms
Neck Fragmentation
M.Di Toro, PI32 Collab.Meeting, Pisa 05
Symmetry Energy
n   p
I
n   p
E(B , )  E(B )  Esym (B )I  O(I )  ...
2
4
Esym
1 2E

2 I 2
I 0
Esym (B) (MeV)
Expansion around
0
Esym
L    0  K sym   B  0 



 a4   B
3  0  18  0 
Pressure & compressibility
L  30
0
1
Pressure gradient
B/0
dPsym
d
2

3
2
1
L  K sym
3
9
Esym
 B
K sym  9 
2
0

 B  0
2
3
0
Esym
 B2
 B  0
Psym
2
Mean Field & Chemical Potentials
symmetry part of the mean field
neutron
proton
neutron-proton chemical potentials
neutron
bulk
proton
neck
124Sn
“asymmetry” I = 0.2
n   p  4Esym ( ) I
STOCHASTIC MEAN-FIELD TRANSPORT
APPROACH
VLASOV + COLLISION and PAULI CORRELATIONS
NPA 642 (1998)
df (r , p, t ) f (r , p, t )

  f , h  I coll  f   I coll
dt
t
2
h
p
U f 
2m
w (1  f )  w f
gain
FLUCTUATIONS
I  0,
f  f ,
 2  (f ) 2
loss
I (t )I (t ' )  2D(t ) (t  t ' )
 (t ) 
1
w  w
Markov
d 2
2 2

  2 D(t )
dt
 (t )
 (teq ) D(teq )  f eq (1  f eq )
Equilibrium in a
2
phase space cell
FLUCT.-DISS.
2D(t )  (1  f )w  f w
OK if
 2   2
Initial:
THEOREM
tot. number of collisions
d
2
2
2






 f 1 f
dt
 (t )
 2  0
(
)
any time
 2  f (1  f
)
 2
Pre-equilibrium Dipole Radiation
Charge Equilibration Dynamics:
Stochastic : Diffusion
vs.
Collective : Dipole Oscillations of the Di-nuclear System  Fusion Dynamics
D0 
Z1Z 2  N1 N 2 
 
(R1  R2 )
A  Z1 Z 2 
D(t) : bremss. dipole radiation
Initial Dipole
- Fusion Dynamics (MassAsymmetry)
- Anisotropy
- Cooling on the way to Fusion
CN: stat. GDR
Pre-equilibrium dipole emission (1)
BNV
Ca + Mo @ 4 AMeV
O20 + Mg20 @ 1 AMeV,
O + Mo @ 4,8,14,20 AMeV
Quantitative: abs. estimations
Simenel et al., PRL86(2001)
TDHF
Baran et al., PRL87(2001)
S32 + Mo100 (6 AMeV)
Pre-equilibrium dipole emission (2)
D(t)
time(fm/c)
S32 + Mo100 (9 AMeV)
@25 AMeV
time(fm/c)
D(t)
M.Papa et al., PRC68(2003)
D.Pierroutsakou et al. (2005)
Cooling in
hot fusion ?
Fusion - Deep Inelastic Competition
Asy-soft
Asy-stiff
E= 30 AMeV , b=0.45 bmax
46Ar
64Ni
+
(1.55)
(1.29)
n-rich
Asy-soft
46V
+
64Ge
Asy-stiff
n-poor
M. Colonna et al., PRC57 (1998)
More fast proton emission
Neck Fragmentation Mechanism
124Sn+124Sn
b=4fm
b=6fm
50AMeV, semi-central
STOCHASTIC
MEAN-FIELD
Time-scale matching:
Instability growth vs Interaction time

Rise and Fall:
-with impact parameter
- with beam energy
Freeze-out
V.Baran et al. NPA 703 (2002)
NECK FRAGMENTATION: COMPRESSIBILITY EFFECTS
the role of volume instabilities
124Sn+64Ni
35AMeV
K=200MEV
b=6fm
K=380MEV
cube of 10fm side
soft
stiff
Central density
evolution
V.Baran et al. NPA 730 (2004)
NECK FRAGMENTATION EVENTS
up-early stage of fragment formation
124Sn+64Ni
; 35AMeV; b=6fm
down- configurations close to freeze-out
Nucleon-nucleon cross sections dependence
free cross sections
half free cross sections
124Sn+64Ni
112Sn+58Ni
P=Nternary/Ntotal
DEVIATIONS FROM VIOLA SYSTEMATICS
r-
ratio of the observed PLF-IMF relative velocity to the
corresponding Coulomb velocity;
r1- the same ratio for the pair TLF-IMF
The Neck-IMF is weakly correlated with both PLF and TLF
Wilczynski-2 plot !
V.Baran, M.Colonna, M.Di Toro NPA 730 (2004)
REDUCED VELOCITY PLOTS:
Note: BNV model
accounts only for the
“prompt” component
of IMF’s
BNV
V. Baran et al. Nucl.
Phys A730 (2004) 329
Chimera 124Sn+64Ni 35AMeV data, same E_loss selections
Gating the reduced plot for light IMFs:
NECK FRAGMENTATION: CM Vz-Vx CORRELATIONS
<0
124Sn
+ 64Ni
35 AMeV
>0
Alignement +
Centroid at  plane  0

Clear Dynamical
Signatures !
Angular distributions: alignment characteristics
Out-of-plane angular distributions
for the “dynamical” (gate 1) and
“statistical” (gate 2) components:
these last are more concentrated in
the reaction plane.
plane is the angle, projected into the reaction
plane, between the direction defined by the
relative velocity of the CM of the system PLFIMF to TLF and the direction defined by the
relative velocity of PLF to IMF
ISOSPIN COMPOSITION OF THE IMF’S
PRODUCED IN NECK FRAGMENTATION:
ASY-EOS EFFECT
124Sn+64Ni
asysoft
35AMeV
124Sn
64Ni
asystiff
superasystiff
NECK ISOSCALING
 = 0.95
Z=1
Z=2
Z=3 Z=4
Z=5
Z=6
Z=7
Z=9
Z=8
Sn 64Ni at 35 MeV/n
112
Sn 58Ni (b=6,7,8fm)
124
asysoft
 0.69
N
asystiff
0.95
V. Baran, M. Colonna, M. Di Toro : NPA 370 (2004) 329
superasystiff
1.10
NECK ISOSCALING
N=7
N=5 N=6
N=8
ln R21
N=4
 = -1.07
Sn 64Ni at 35 MeV/n
112
Sn 58Ni (b=6,7,8fm)
124
asysoft
 -0.67
N=2
N=3
Z
asystiff superasystiff
-1.07
-1.16
58Fe+58Fe vs. 58Ni+58Ni b=4fm
47AMeV:
Freeze-out Asymmetry distributions
Fe


Ni
Ni
Fe
Fe: fast neutron emission
Ni: fast proton emission
White circles: asy-stiff
Black circles: asy-soft
Asy-soft: small isospin migration
R.Lionti et al., nucl-th/0501012
Neck Fragments: N/Z – angle correlation
FeFe vs NiNi b=4fm 47AMeV: 40% ternary
- Isospin Migration for almost symmetric systems
- Minimum N/Z around 90° : earlier formation?
R.Lionti et al, nucl-th/0501012
FeFe b=4fm 47AMeV: density contour plots
fm/c
R.Lionti et al.
nucl-th/0501012
PLF/TLF residues asymmetry (N-Z)/A
System
initial
t=100fm/c(after pre-eq)
freeze-out
58Fe+58Fe
1.23
1.22
1.23 binary
1.19 ternary
58Ni+58Ni
1.07
1.12
1.17 binary
1.12 ternary
n-enrichment of
Neck-Fragments
even for symmetric
systems!