Maria Colonna Laboratori Nazionali del Sud (Catania )
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Transcript of Maria Colonna Laboratori Nazionali del Sud (Catania )
Energy functional of asymmetric nuclear matter:constrain the iso – EOS (symmetry energy)Information on the behaviour of the symmetry energy at sub-saturation and super-saturation densities
Phase transitions in finite systems:phase diagram of exotic systems & new features of the fragmentation mechanism
Important implications in the astrophysical context:neutron star crust, supernova explosion (clustering of low-density matter)Important for studies of the structure of exotic nuclei
What can we learn from reactions at intermediate energy (30-100 MeV/A) with exotic beams ?
Isospin Transport: the density dependent Esym
I
EIEjj sym
sympn
)()(
IDDj
IDDjIppp
Innn
currents
diffusion
Diffusion Drift
drift
pnqI
D
D
T
qIq
TI
,,
,
Direct Access to Value and Slope of the Symmetry Energy at ρ !
E/A (ρ) = Es(ρ) + Esym(ρ)I²I=(N-Z)/A
IEsympn 4
Self-consistent mean-field calculations
asy-soft
asy-stiff
124Sn “asymmetry” = 0.2
Symmetry Potentials and Effective Masses
neutron
proton
Asy-stiffAsy-soft
Lane Potentials
**pn mm
**pn mm
Density dependence Momentum dependence1
2
*
1
k
Uk
mmm qq
(Un-Up)/2I
Phys.Rep.410(2005)335-466
Symmetry energy parameterizations are implemented into transportcodes (Stochastic Mean Field - SMF)
Observables related to isospin diffusion and drift:isospin equilibration (imbalance ratio) , isospin migration(neck composition)
Observables related to n-p effective mass splitting: high pt distribution of pre-equilibrium emission,collective flows, light clusters
Disantangle isovector effects from isoscalar effects Better focus on iso-EOS
The density-dependent symmetry energy and n-p effective mass splitting: Observables
b=8f
mb=
10fm
ISOSPIN DIFFUSION AT FERMI ENERGIES124Sn + 112Sn at 50 AMeV
SMF - transport modelb=8fmb=9 fmb=10fm
120fm/c100fm/c80fm/c
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R;
IIIII2R
experimental data(B. Tsang et al. PRL 92 (2004) )
asysoft eos superasystiff eos
contact time
Baran, Colonna, Di Toro, Pfabe, Wolter, PRC72(2005)
Imbalance ratios
asy-soft EOS –faster equilibration
Imbalance ratios: isoscalar vs. isovector effects
If:
then:
β = (N-Z)/A τ symmetry energy tcontact dissipation
Kinetic energy loss as a measure of dissipation (time of contact)
R dependent only on the isovector part of the interaction !
MD, MI: isoscalar effective forces
Isospin migration in neck fragmentation
Transfer of asymmetry from PLF and TLF to the low density neck region
Effect related to the derivative of the symmetryenergy with respect to density
PLF, TLF
neck
emittednucleons
ρ1 < ρ2
Asymmetry flux
asy-stiff
asy-soft
Larger derivative with asy-stiff larger isospin migration effects
Sn112 + Sn112
Sn124 + Sn124
b = 6 fm, 50 AMeVDensity gradients derivative of Esym
arXiv:0711.3761
ρI < ρR
Asymmetry flux
AAres
Isospin exchange: βIMF / βres ratioNeck mass A, asymmetry β + ΔβResidues mass Ares, asymmetry β – Δβ A/Ares
minimizing symmetry energy variation
MD MI
stiff - - soft
This ratio depends onlyon the symm. energy variation around the neck density
It should also be studiedas a function of dissipationor observables connected to the density (IMF multiplicity …)
< 0
Sn112 + Sn112 Sn124 + Sn124
b = 6 fm, 50 AMeV
J.Rizzo et al., PRC 72 (2005) → Isotope Science Facility at MSU, White Paper 2006
Gas asymmetry vs. p_t 8/0
Light isobar (3H/3He) yields
Mass splitting: N/Z of Fast Nucleon Emission
High p_t “gas” asymmetry: Observable very sensitive to the mass splitting and not to the asy-stiffness
Vs. Kinetic Energies
132Sn+124Sn, 100 AMeV, b=2 fm, y(0)0.33H/3Hen/p
asy-stiffasy-stiff
124Sn+124Sn, 50 AMeV, b=2 fm
• m*n>m*p• m*n<m*p
Collective flowsIn-plane Out-of-plane
yyx
yxt pp
pppy 22
22
2 ),(V
ytxt pppyV /),(1
tnt
pt
np pVpVpV 111 )(V)(V)(V n2
p2
n-p2 ttt ppp
1 < V2 < +1
X
Z
y = rapiditypt = transverse momentum
= 1 full outV2 = 0 spherical = + 1 full in
Differential flows)(1),(1
),(1),(
pn
pyvZN
pyv
i
tiitalDifferenti
B-A Li et al. PRL2002
Au+Au 250 AMeV, b=7 fm
m*n<m*p : larger neutron squeeze out at mid-rapidity
Z=1 data, M3 centrality, 6<b<7.5fm
**pn mm
Mass splitting: Elliptic Flow Difference
129Xe+124Sn,100AMeV
124Xe+112Sn,100AMeV
m*n < m*p
m*p < m*n
Triton/He3 Transverse flow ratioMSU/RIA05, nucl-th/0505013 , AIP Conf.Proc.791 (2005) 70
Validate the mechanisms investigated and the conclusionsdrawn from the study of symmetric matter (multifragmentation)
New features: Instabilities in asymmetric systems (phase diagram)
New features: Isospin distillationObservables: isoscaling, fragment <N>/Z at break-up, double ratiosDistillation in presence of radial flow <N>/Z vs. Ekin
Phase transitions in exotic systems: new effects
DensityTe
mpe
ratu
re
τ = 100 fm/c τ = 50 fm/c
The width of the spinodal zone should depend on isospin
Colonna et al., PRL2002Level density, limiting temperature …
Isospin-dependent phase transition
Isospin distillation: the liquid phase is more symmetric than the gas phase
β = 0.2
β = 0.1
Non-homogeneous density
Spinodal decomposition in a box asy-stiff - - -asy-soft
F.Matera, in preparation
asy-soft
asy-stiff
Density gradients derivative of Esym
Increased distillationout of equilibrium
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132E/A = 50 MeV, b=2 fm
N = Σi Ni , Z = Σi Zi 3≤ Zi ≤ 10 asy-stiff - - -asy-soft
Proton/neutron repulsion:larger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy 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-EoSis observed in the double N/Zs ratio If N/Zfin = a(N/Z +b), N/Zs not affected by secondary decay !
Different radial flows for neutrons and protonsFragmenting source with isospin gradient N/Z of fragments vs. Ekin !
Dou
ble
ratio
s
Central collisions
pn
r
arXiv:0707.3416
Conclusions and Perspectives -I-
Reactions with exotic beams at intermediate energy are very important for the study of fundamental properties of nuclear matter:
The “elusive” symmetry energy behaviour far from normal density
Phase diagram of finite nuclei and Phase transitions
Good observables have been proposed:
Imbalance ratio, neck neutron enrichment, isotopic content of pre-equilibrium emission (pt dependence), differential flows, isoscaling, isospin distillation, N/Z vs. Ekin.Isospin effects are enhanced by increasing the system asymmetry.
Need to enlarge the systematics of data (and calculations) to validate the current interpretation and the extraction of Esym (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)
Conclusions and Perspectives -II-
γ
Isospin distillation in presence of radial flow Sn112 + Sn112 Sn124 + Sn124 Sn132 + Sn132E/A = 50 MeV, b=2 fm
N = Σi Ni , Z = Σi Zi 3≤ Zi ≤ 10 asy-stiff - - -asy-soft
Proton/neutron repulsion:larger negative slope in the stiff case(lower symmetry energy) n-rich clusters emitted at largerenergy 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-EoSis observed in the double N/Zs ratio If N/Zfin = a(N/Z +b), N/Zs not affected by secondary decay !
Different radial flows for neutrons and protonsFragmenting source with isospin gradient N/Z of fragments vs. Ekin !
Dou
ble
ratio
s
Central collisions
pn
r
Transverse flow of light clusters: 3H vs. 3He
m*n>m*p m*n<m*p
129Xe+124Sn, 100AMeV 124Xe+112Sn, 100AMeV
Larger 3He flow (triangles) Coulomb effects
Larger differencefor m*n>m*p
Triton/Helium transverse flow ratio:smaller for m*n>m*p
Good sensitivity to the mass splitting
dppddp )sin(,,Set of coordinates
)sin( p = 260 MeV/c, Δp = 10 MeV/c,
t = 0 fm/c t = 100 fm/c
)cos(3
23
pV
The variance of the distribution function
p = 190 MeV/c Δθ = 30°
spherical coordinates fit the Fermi sphere allow large volumes
Clouds position
Best volume: p = 190 MeV/c, θ = 20°12.0)(2 Ff E
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
Wilczynski-2 plot !
124Sn + 64Ni 35 AMeV
v_z (c)
v_x
(c)
Distribution after secondary decay (SIMON)
Sn124 + Sn124, E/A = 50 MeV/A, b = 6 fm
CM Vz-Vx CORRELATIONS
v_par
58Fe+58Fe vs. 58Ni+58Ni b=4fm 47AMeV:Freeze-out Asymmetry distributions
Fe
Ni
Fe Ni
White circles: asy-stiffBlack circles: asy-soft
Asy-soft: small isospin migration
Fe: fast neutron emission
Ni: fast proton emission
Angular distributions: alignment characteristics
plane is the angle, projected into the reaction plane, between the direction defined by the relative velocity of the CM of the system PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF
Out-of-plane angular distributions for the “dynamical” (gate 2) and “statistical” (gate 1) components: these last are more concentrated in the reaction plane.
Dynamical Isoscaling
Z=1
Z=7
primary
final
yieldionlightSnSn
112
124
AZNR
AfZNY
12221
2
2
2ln
)(exp)(),(
not very sensitive to Esym ?124Sn Carbon isotopes (primary)
AAsy-soft
Asy-stiffT.X.Liu et al.
PRC 2004
50 AMeV
(central coll.)
I = Iin + c(Esym, tcontact) (Iav – Iin), Iav = (I124 + I112)/2
RP = 1 – c ; RT = c - 1
112112T
124124T
112112T
124124T
MT
T112112P
124124P
112112P
124124P
MP
P IIIII2R;
IIIII2R
Imbalance ratios
If:
then:
50 MeV/A 35 MeV/A
• Larger isospin equilibration with MI
(larger tcontact ? ) • Larger isospin equilibration with asy-soft (larger Esym)• More dissipative dynamics at 35 MeV/A
124Sn + 64Ni 35 AMeV ternary events
N/Z vs. Alignement Correlation in semi-peripheral collisions
Experiment Transp. Simulations (124/64)
Chimera data: see E.De Filippo, P.Russotto NN2006 Contr., Rio
Asystiff
Asysoft
V.Baran, Aug.06
Asystiff: more isospin migration to the neck fragments
Histogram: no selection
E.De Filippo et al. , PRC71(2005)
φ
vtra