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Nuclear Matter and Nuclear Dynamics
Maria Colonna
Laboratori Nazionali del Sud (Catania)
XII Convegno su Problemi di Fisica Nucleare Teorica
Cortona, 8-10 Ottobre 2008
 The EOS of symmetric and neutron matter from many-body theories:
the energy functional is calculated from the bare nucleon-nucleon interaction
 Information on Esym behavior from Heavy Ion Collisions
Transport theories
 High density EOS: implications on the structure of neutron stars
 Transition to the QGP ?
Role of isospin
BBG calculations with two- and three-body forces
The energy functional is calculated from the bare nucleon-nucleon interaction
Microscopic three-body force(TBF) exchange diagrams on
the basis of
mesons, incorporating Δ, Roper,
nucleon-antinucleon excitations
TBF consistent with the underlying two-nucleon
One Boson Exchange potential
Results for EOS and symmetry energy
Bonn B
Nijmejen potential
Argonne v18 potential
phenomenological
Urbana type TBF
EOS symm. matter
Phenomenological Urbana type TBF
Stiffer EOS with TBF
Similar EOS
v18
Bonn B
Constraints on pressure from
Baldo,Shaban, PLB661(08)
nuclear flow data analysis
The overall effect of the same TBF
on the EOS can be different according
to the
adopted
Li, two-body
Lombardo,force
Schulze,
Zuo, PRC 2008
Li, Lombardo, Schulze, Zuo, PRC77(08)
EOS of Symmetric and Neutron Matter
Symmetric Matter | Symmetry Energy | Neutron Matter
asy-stiff
NLρδ
BOB
asy-soft
Urbana
NLρ
DD-F
Slope at normal density:
Isospin transport at Fermi energies
Dirac-Brueckner
RMF
Density-Dependent couplings
AFDMC
S.Gandolfi et al. , PRL98(2007)102503
Constraints from
compact stars & heavy ion data
T.Klaehn et al. PRC 74 (2006) 035802
Effective parameterizations
of symmetry energy
Transport codes
Nuclear Dynamics
Astrophysical problems
Extracting information on the symmetry energy
from terrestrial lab.s
Nuclear Dynamics
Transport equations
Fermi energies, 10-60 MeV/A (below and around normal density):
 GDR
 Charge equilibration
 Fragmentation in exotic systems
Intermediate energies, 0.1-0.5 GeV/A (above normal density):
 Meson production (pions, kaons)
 Collective response (flows)
Phys. Rep. 389 (2004)
Phys.Rep.410(2005)335
High density behavior
Neutron stars
Semi-classical approach to the many-body problem
Time evolution of the one-body distribution function
Vlasov
Boltzmann
f ( r , p, t )
Langevin

f (r , p )  h( f ), f (r , p )  K ( f )  K (r , p, t )
t
Vlasov: mean field
2
pi
h( f )  
U ( f )
i 2m
Boltzmann: average collision term
df
 fW   fW 
dt
Vlasov Boltzmann
Langevin
Loss term
Langevin: random
walk in phase-space
D(p,p’,r)
Ensemble average
Fluctuation variance:
D(p,p’,r)
w
σ2f = <δfδf>
SMF model : fluctuations projected onto ordinary space
density fluctuations δρ
Collective excitations
Charge equilibration
Relativistic nuclear excitation of GDR
in the target in semi-peripheral collisions
Dasso,Gallardo,Lanza,Sofia, NPA801(2008)129
Equations of motion for n and p centroids
obtained from Einstein’s set
- Restoring force
- Coulomb + nuclear excitation (Wood-Saxon)
(neutron skin)
Zrel = zn – zp
Xrel = xn - xp
Larger amplitude due to nuclear field
one-phonon
two-phonon
P(b): probability for a given reaction channel
T(b): attenuation factor due to depopulation of reaction channels
Pre-equilibrium Dipole Radiation
Charge Equilibration Dynamics:
Stochastic → Diffusion
vs.
Collective → Dipole Oscillations of the Di-nuclear System  Fusion Dynamics
Initial Dipole
D0 
Z1Z 2  N1 N 2 
 
R1  R2 
A  Z1 Z 2 
D(t) : bremss. dipole radiation
CN: stat. GDR
36Ar
+ 96Zr
40Ar + 92Zr
Symmetry energy
- Isovector Restoring Force
below saturation
- Neutron emission
- Neck Dynamics (Mass Asymmetry)
- Anisotropy
Experimental evidence of the extra-yield
- Cooling on the way to Fusion
LNS data
B.Martin et al., PLB 664 (2008) 47
Isospin gradients: Pre-equilibrium dipole emission


NZ
1
X p (t )  X n (t )  X p ,n 
xip ,n
A
Z, N
1
DK (t )  Pp  Pn  Pp ,n 
pip ,n
Z, N
D, DK   i
D(t ) 
SPIRALS → Collective Oscillations!
TDHF: C.Simenel, Ph.Chomaz, G.de France
132Sn + 58Ni
124Sn + 58Ni
Bremsstrahlung:
Quantitative estimations
2
2
dP
2e
 NZ  ''


 D ( )
3
dE 3c E  A 
2
V.Baran, D.M.Brink, M.Colonna, M.Di Toro, PRL.87(2001)
arXiv:0807.4118
Larger restoring force with asy-soft
larger strength !
ISOSPIN DIFFUSION AT FERMI ENERGIES
124Sn
112Sn
at 50 AMeV
b=8fm
SMF - transport model
calculations
+
Time
Imbalance ratios
M
H
L
+
124Sn +
112Sn +
112Sn
124Sn
112Sn
experimental data (B. Tsang et al. PRL 92 (2004) )
x = β = (N-Z)/A
τ
symmetry energy Esym
Smaller R for larger Esym
tcontact
energy dissipation
124Sn
Several isoscalar
interactions
M
124Sn
+
112Sn
H
L
124Sn
+
112Sn +
124Sn
112Sn
Kinetic energy loss
Rizzo, Colonna, Baran, Di Toro, Pfabe, Wolter, PRC72(2005) and
J.Rizzo et al. NPA806 (2008) 79
Unstable dynamics
Liquid-gas phase transition
Fragmentation in exotic systems
Stochastic mean field (SMF) calculations
(fluctuations projected on ordinary space)
b = 4 fm
b = 6 fm
Central collisions
Ni + Au, E/A = 45 MeV/A
Sn124 + Sn124, E/A = 50 MeV/A
Isospin-dependent liquid-gas phase transition
Isospin distillation: the liquid phase is more symmetric than the gas phase
Density gradients
derivative of Esym
asy-stiff
asy-soft
asy-stiff
- - -asy-soft
Spinodal decomposition in a box (quasi-analytical calculations)
arXiv:0707.3416
Non-homogeneous
density
β = 0.2
β = 0.1
asy-soft
β = 0.1
asy-stiff
β = 0.2
N/Z and variance decrease
in low-density domains
Isospin “tuning”
Correlations of N/Z vs. Ekin
Cluster density
Colonna & Matera, PRC77 (08) 064606
arXiv:0707.3416
Isospin migration in neck fragmentation
Asymmetry flux
 Transfer of asymmetry from PLF and TLF to
the low density neck region
LNS data – CHIMERA coll.
 Effect related to the derivative of the symmetry
energy with respect to density
ρ 1 < ρ2
Density gradients
b = 6 fm, 50 AMeV
derivative of Esym
asy-stiff
PLF, TLF
neck
emitted
nucleons
Vrel/VViola (IMF/PLF)
Experimental evidence of
n-enrichment of the neck:
Correlations between N/Z
and deviation from Viola
systematics
asy-soft
Larger derivative with asy-stiff
larger isospin migration effects
Sn112
+ Sn112
Sn124
+ Sn124
E.De Filippo et al.,
PRC71,044602 (2005)
E.De Filippo et al. NUFRA 2007
J.Rizzo et al. NPA806 (2008) 79
Reactions at intermediate energies:
Information on high density behavior
of Esym
Quantum Hadrodynamics (QHD) → Relativistic Transport Equation (RMF)
OBE
NN scattering
nuclear interaction from meson exchange:
main channels (plus correlations)
0,0 1,0
0,1 r1,1
Scalar
Vector
Scalar
Isoscalar
Vector
Isovector
Nuclear interaction by Effective Field Theory
as a covariant Density Functional Approach
Saturation
Attraction & Repulsion
 
 
 

1
1
1
L     i   gVˆ   M  g Φˆ   Φˆ  Φˆ  m2 Φˆ 2  WˆWˆ   m2VˆVˆ 
2
4
2
 :      m2 Φˆ  g ψψ  g ρˆ S
 :  Wˆ

ˆ

 mV  g ψ ψ  g J
2

Relativistic structure also
in isospin space !
Esym= kin. + (rvector) – ( scalar)
RBUU transport equation
Wigner transform ∩ Dirac + Fields Equation
Relativistic Vlasov Equation
+ Collision Term…
Vector field
ki*  ki   i
mi*  M   s ,i
drift
mean field
Scalar field
F         



f
p 
  r f  rU   p f  I coll
t m
Non-relativistic Boltzmann-Nordheim-Vlasov
“Lorentz Force”→ Vector Fields
mean-field + pure relativistic term
Collision term:
Self-Energy contributions to the inelastic channels!
Au+Au central: π and K yield ratios vs. beam energy
2
 M*  
1 k F2 1 
Esym 
  f r  f  *   r B
6 EF*2 2 
 E  

NLρδ
NLρ
f r ,
g
  r ,
m
 r ,




2
RMF Symmetry Energy: the δ -mechanism
NL
Effects on particle production
Kaons:
~15% difference between
DDF and NLρδ
132Sn+12
4Sn
Pions: large effects at lower energies
Inclusive multiplicities
G.Ferini et al.,PRL 97 (2006) 202301
Collective (elliptic) flow
Out-of-plane
V2 ( y, pt ) 
px2  p y2
px2  p y2
y
1 < V2 < +1
V2
=  1 full out
= 0 spherical
= + 1 full in
High pT selection
V2p-n ( pt )  V2p ( pt )  V2n ( pt )
Differential flows
V.Giordano, Diploma Thesis
m*n<m*p : larger neutron squeeze out
at mid-rapidity
 vDifferential ( y, pt ) 
 i  1(n),1( p)
1
N Z
 v ( y , p )
i i
t
B-A Li et al. PRL2002
Measure of effective masses in high density – highly asymmetric matter !
Neutron stars as laboratories for the study
of dense matter
Facts about Neutron Stars :
• M ~ 1 to 2M0 ( M0=1.998·1033g)
• R ~ 10 Km
• N obs. Pulsars - 1500
Peng,Li,Lombardo, PRC77 (08) 065807
• P > 1.58 ms (630 Hz)
• B = 108 ÷ 1013 Gauss
H

( r BH , r3H , T )   BQ ( r BQ , r3Q , T )
B
inner core:
3H (....)  3Q (....)
r = 1/fm3  dNN=1 fm
H
H
H
Q
Q
Q
hadron-to-quark transition ! P ( r B , r3 , T )  P ( r B , r 3 , T )
CDDM model
Density dependent quark mass
Bonn B
Gibbs equilibrium
condition +
density and charge
conservation
Tolmann-Oppenheimer-Volkov equation
Conclusions:
1) transition to quark phase reduces the
maximum mass to values similar to
data
2) results very sensitive to the
Neutron Star Mass-Radius Diagram
confinement parameter D
Hybrid stars
Schulze et al.
Tolmann-Oppenheimer-Volkov equation
dP
m
P
4P r 3
2 m 1
  2 (1  )(1 
)(1 
)
dr

m
r
r
dm
 4r 2
dr
Baryonic EOS including hyperons
 soft EOS
MG/M0 about 1.5 at finite T
too small masses for NS at T = 0
 Metastability of hot PNS
Including quarks:
MG/M0 about 1.5
 no metastable hybrid PNS
 Rather low limiting masses of PNS
NJL: the onset of the pure quark phase in the
inner core marks an instability
 No transition to quarks with hyperons
 smaller masses than NS, no metastability
 masses around 1.8
Nicotra, Baldo, Burgio, Schulze, PRD74(06)123001
Burgio & Plumari, PRD77(08)085022
Serious problems for our understanding of
the EOS if large masses (about 2) are observed !
EOS of low-density neutron matter
Inner crust of NS: nuclear lattice permeated by a gas of neutrons
At a given point nuclei merge and form more complicated structures
Study of EOS of pure neutron matter
QMC
M.Baldo & C. Maieron, PRC 77, 015801 (2008)
- Only s-wave matters, but the “unitary limit” is actually
never reached. Despite that the energy is ½ the kinetic energy
in a wide range of density (for unitary 0.4-0.42 from QMC).
- The dominant correlation comes from the Pauli operator
- Scattering length and effective range determine
completely the G-matrix.
- Variational calculations are slightly above BBG.
Good agreement with QMC.
- Both three hole-line and single particle potential effects are small
and essentially negligible. Three-body forces negligible.
In this density range one can get the “exact” neutron matter EOS
Phases of Nuclear Matter
200
Big Bang
Plasma of
Quarks and
Isospin ?
MeV
Gluons
Temperature
20
Collisions
Ion
Mixed Phase
In terrestrial
Labs.?
Heavy
Gas
Liquid
Density r/r0
1: nuclei
N eutron
Stars
5?
Philippe Chomaz artistic view
Mixed phase in
terrestrial labs ?
In a C.M. cell
U 238U ,1AGeV
238
b  7 fm
Exotic matter over 10 fm/c ?
T.Gaitanos, RBUU calculations
Testing deconfinement with RIB’s?
B1/4 =150 MeV
NLρ
r B  (1   ) GM3
r BH  r BQ
NLρδ
r 3  (1   ) r 3H  r 3Q
symmetric
neutron
QuarkBag model
(two flavors)
Hadron-RMF
rtrans
1 AGeV
300 AMeV
Trajectories of
132Sn+124Sn, semicentral
onset of the mixed phase
→ decreases with asymmetry
Signatures?
M. Di Toro
Symmetry energies:
- Large variation for hadron EOS
- Quark matter: Fermi contribution only
Neutron migration to the quark clusters (instead of a fast emission)
Drago,Lavagno, Di Toro, NPA775(2006)102-126
Crucial role of symmetry energy
in quark matter !
QGP dynamics
Quark dynamics in the QGP phase
RHICS discoveries:
We have not just a bunch of particles, but a
transient state of high energy plasma with
Strong collective phenomena (elliptic flow v2) in
condition similar to those 10-5 s after
the Big Bang
~15 GeV/fm3 >> c T~ 350 MeV
(according to hydrodynamical calculations)
z
y
x
 x
y 2  x2
y x
2
v2  cos2 
2
- The plasma is not a so perfect fluid …
(hydrodynamical) scaling of v2 not observed
- Importance of parton coalescence
But finite mean free path
call for a transport approach!
p


p x2  p y2
p x2  p y2
Perform a Fourier expansion of the
momentum space particle distributions
dN
dN 


1

2
v
cos(
n

)
n n

dpT d dpT 

 
   p F   m  m  p* f ( x, p )  I 22  I 23  ...
Parton cascade
No freeze-out
Finite cross section calculations
corresponding to constant finite shear viscosity
(quantum limit) can reproduce experimental features
h/s=1/4
No freeze-out
Quantum mechanism h/s > 1/15 :
Kinetic Theory
h
E  t  1
1
  p λ  3T    1
s 15
v2/ε scaling broken, v2/<v2>
scaling reproduced
what about v2 absolute value?
v2(pT) as a measure of h/s
h/s  0.1-0.2 + freeze-out
Open the room to need
coalescence in the region
of Quark Number Scaling
Ferini et al., 0805. 4814 [nucl-th]
Kinetic approach to relativistic heavy ion collisions
Ab initio partonic transport code
Total cross section
p-p collisions
Predictions for rapidity distributions at LHC
…with the possibility to include an LQCD
inspired mean-field based on the Bag model
Calculations for nuclear matter inside a box
Conclusions and Perspectives
Reactions with exotic beams at intermediate energy are
important for the study of fundamental properties of
nuclear matter:
The “elusive” symmetry energy behavior far from normal density
γ
(consensus on Esym~(ρ/ρ0) with γ~0.7-1 at low density)
Evidences from Giant Monopole Resonance in 112-124Sn isotopes
T.Li et al, PRL99(2007)162503
Still large uncertainties at high density
Cross-check with the predictions of BBG theory
High density behavior
neutron stars
Transition to the quark phase ? Role of isospin to be investigated
Quark dynamics in the QGP phase, collective flows and
hadronization mechanisms in UrHIC
Rotation on the Reaction Plane of the Emitting Dinuclear System
Dynamical-dipole emission
ΔΦ=2 → x=0 → a2=-1/4 : Statistical result,
Collective Prolate on the Reaction Plane
Charge equilibrium
Φi
Φf
Average over reaction planes:
Beam Axis
1 3 
W ( )  W0 1  a2 P2 (cos ), a2    x 
4 4 
sin()
x  cos( i   f )
,    f   i

θγ : photon angle vs beam axis

ΔΦ=0 → Φi =Φf = Φ0

W ( )  1 (1 sin 2 0 )P2 (cos )
36Ar+96Zr vs. 40Ar+92Zr: 16AMeV Fusion
events: same CN selection
All probed
Rotating angles
No rotation: Φ0=0 → sin2θγ pure dipole
Angular distribution of the
extra-yield (prompt dipole):
anisotropy !
Martin et al.
Simulations
Accurate Angular Distrib. Measure:
Dipole Clock!
Central collisions
 Sn112 + Sn112
 Sn124 + Sn124
 Sn132 + Sn132
E/A = 50 MeV, b=2 fm
Isospin distillation in presence of radial flow
Different radial flows for neutrons and protons
Fragmenting source with isospin gradient
N/Z of fragments vs. Ekin !
n
p
Double ratios (DR)
3≤ Zi ≤ 10
N = Σi Ni , Z = Σi Zi
asy-stiff
- - -asy-soft
r
DR = (N/Z)2 / (N/Z)1
 Proton/neutron repulsion:
larger negative slope in the stiff case
(lower symmetry energy)
 n-rich clusters emitted at larger
energy in n-rich systems
To access the variation of N/Z vs. E:
“shifted” N/Z: N/Zs = N/Z – N/Z(E=0)
Larger sensitivity to the asy-EoS
is observed in the double N/Zs ratio
If N/Zfin = a(N/Z +b), N/Zs not affected by secondary
decay !
arXiv:0707.3416
Conclusions: optimistic?
Last page (252!) of the review
“Recent Progress and New Challenges in Isospin Physics with HIC”
Bao-An Li, Lie-Wen Chen, Che Ming Ko
ArXiv:0804.3580, 22 Apr 2008 (Phys. Rep. 464 (2008) 113-281)
Chimera-LAND
at GSI ?
Samurai Int. Coll.
at RIKEN?
Exotic Beams at FAIR?
Conclusions and Perspectives -II Need to enlarge the systematics of data (and calculations) to
validate the current interpretation and the extraction of Esym
γ
(consensus on Esym~(ρ/ρ0) with γ~0.7-1 at low density)
Still large uncertainty at high density
 It is important to disantangle isovector from isoscalar effects.
Cross-check of “isoscalar” and “isovector” observables
V.Baran (NIPNE HH,Bucharest) M.Di Toro, J. Rizzo (LNS-Catania)
F. Matera (Florence) M. Zielinska-Pfabe (Smith College)
H.H. Wolter (Munich)
Central collisions
 Sn112 + Sn112
 Sn124 + Sn124
 Sn132 + Sn132
E/A = 50 MeV, b=2 fm
Isospin distillation in presence of radial flow
Different radial flows for neutrons and protons
Fragmenting source with isospin gradient
N/Z of fragments vs. Ekin !
n
p
r
Double ratios
3≤ Zi ≤ 10
N = Σi Ni , Z = Σi Zi
asy-stiff
- - -asy-soft
 Proton/neutron repulsion:
larger negative slope in the stiff case
(lower symmetry energy)
 n-rich clusters emitted at larger
energy in n-rich systems
To access the variation of N/Z vs. E:
“shifted” N/Z: N/Zs = N/Z – N/Z(E=0)
Larger sensitivity to the asy-EoS
is observed in the double N/Zs ratio
If N/Zfin = a(N/Z +b), N/Zs not affected by secondary
decay !
Transverse flow of light clusters: 3H vs. 3He
129Xe+124Sn,
100AMeV
124Xe+112Sn,
100AMeV
m*n>m*p
m*n<m*p
Larger 3He flow
(triangles)
Coulomb effects
Larger difference
for m*n>m*p
Triton/Helium transverse flow ratio:
smaller for m*n>m*p
Good sensitivity to the mass splitting
The variance of the distribution function
spherical coordinates
 fit the Fermi sphere
 allow large volumes
p3
V  2
 cos( )
3
 2f (EF )  0.12
Δθ = 30°
p = 190 MeV/c
Clouds position
Best volume: p = 190 MeV/c, θ = 20°
Set of coordinates dp, pd, p sin( )d
t = 0 fm/c
t = 100 fm/c
p = 260 MeV/c, Δp = 10 MeV/c, h  sin( )
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 IMF is weakly correlated with both PLF and TLF
124Sn
+ 64Ni
35 AMeV
Wilczynski-2 plot !
CM Vz-Vx CORRELATIONS
v_par
Sn124 + Sn124,
E/A = 50 MeV/A, b = 6 fm
Distribution after secondary
decay (SIMON)
v_z (c)
58Fe+58Fe vs. 58Ni+58Ni b=4fm
47AMeV:
Freeze-out Asymmetry distributions
Fe


Ni
Fe
Fe: fast neutron emission
Ni: fast proton emission
Ni
White circles: asy-stiff
Black circles: asy-soft
Asy-soft: small isospin migration
Details of SMF model
• Correlations are introduced in the time evolution of the one-body density: ρ
ρ +δρ
as corrections of the mean-field trajectory
• Correlated density domains appear due to the occurrence of mean-field (spinodal)
instabilities at low density
Fragmentation Mechanism: spinodal decomposition
T
gas
Is it possible to reconstruct fragments and calculate their properties only from f ?
liquid
ρ
Extract random A nucleons among test particle
distribution
Coalescence procedure
Check energy and momentum conservation
A.Bonasera et al, PLB244, 169 (1990)
Liquid phase: ρ > 1/5 ρ0
Fragment
Neighbouring cells are connected
Recognition
(coalescence procedure)
Fragment excitation energy evaluated by subtracting
Fermi motion (local density approx) from Kinetic energy
 Several aspects of multifragmentation in central and semi-peripheral collisions well
reproduced by the model
Chomaz,Colonna, Randrup Phys. Rep. 389 (2004)
 Statistical analysis of the fragmentation path
 Comparison with AMD results
Baran,Colonna,Greco, Di Toro Phys. Rep. 410, 335 (2005)
Tabacaru et al., NPA764, 371 (2006)
A.H. Raduta, Colonna, Baran, Di Toro, ., PRC 74,034604(2006)
PRC76, 024602 (2007)
Rizzo, Colonna, Ono, PRC 76, 024611 (2007)
i
Angular distributions: alignment characteristics
Out-of-plane angular distributions
for the “dynamical” (gate 2) and
“statistical” (gate 1) 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
Dynamical Isoscaling
124
Sn
light ion yield
112
Sn
primary
50 AMeV
Z=1
(central coll.)
Z=7
final
 (   ) 

Y ( N , Z )  f ( A) exp  
2



2
N Z
 ln R21  2  2  1 


 A 
2
T.X.Liu et al.
PRC 2004
not very sensitive to Esym ?
124Sn
Carbon isotopes (primary)
Asy-stiff
Asy-soft
A
Imbalance ratios
124124
112112
M
124124
112112
2I M

I

I
2
I

I

I
R P  P 124P124 112P112
; R T  T 124T124 112T112
IP
 IP
IT
 IT
If:
I = Iin + c(Esym, tcontact) (Iav – Iin),
then:
RP = 1 – c ;
Iav = (I124 + I112)/2
RT = c - 1
50 MeV/A
• Larger isospin equilibration with MI
(larger tcontact ? )
• Larger isospin equilibration with asy-soft
(larger Esym)
• More dissipative dynamics at 35 MeV/A
35 MeV/A
N/Z vs. Alignement Correlation in semi-peripheral collisions
vtra
φ
124Sn
Experiment
Histogram:
no selection
+ 64Ni 35 AMeV ternary events
Transp. Simulations (124/64)
Asystiff
Asysoft
Chimera data: see E.De Filippo, P.Russotto
NN2006 Contr., Rio
E.De Filippo et al. , PRC71(2005)
Asystiff: more isospin migration to the neck fragments
V.Baran, Aug.06
Mass splitting: Transverse Flow Difference
Au+Au 250 AMeV, b=7 fm
mn*  m*p
Difference of n/p flows
Larger effects at high momenta
Triton vs. 3He Flows?
Z=1 data
M3 centrality
6<b<7.5fm
MSU/RIA05, nucl-th/0505013 , AIP Conf.Proc.791 (2005) 70