Maria Colonna Laboratori Nazionali del Sud (Catania) Dynamics and Thermodynamics with

 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 ( MeV/A) with exotic beams ?

The density-dependent symmetry energy and n-p effective mass splitting

Isospin Transport: the density dependent E sym currents diffusion DiffusionDrift drift Direct Access to Value and Slope of the Symmetry Energy at ρ ! E/A (ρ) = E s (ρ) + E sym (ρ)I ² I=(N-Z)/A Self-consistent mean-field calculations asy-soft asy-stiff

124 Sn “asymmetry”  = 0.2 Symmetry Potentials and Effective Masses neutron proton Asy-stiff Asy-soft Lane Potentials Density dependence Momentum dependence (Un-Up)/2I Phys.Rep.410(2005)

 Symmetry energy parameterizations are implemented into transport codes (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 p t 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=8fm b=10fm ISOSPIN DIFFUSION AT FERMI ENERGIES 124 Sn Sn at 50 AMeV SMF - transport model b=8fm b=9 fm b=10fm 120fm/c 100fm/c 80fm/c 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 t contact 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 symmetry energy with respect to density PLF, TLF neck emitted nucleons ρ 1 < ρ2ρ2 Asymmetry flux asy-stiff asy-soft Larger derivative with asy-stiff larger isospin migration effects Sn112 + Sn112 Sn124 + Sn124 b = 6 fm, 50 AMeV Density gradients derivative of E sym arXiv:

ρ I < ρRρR Asymmetry flux A A res Isospin exchange: β IMF / β res ratio Neck mass A, asymmetry β + Δβ Residues mass A res, asymmetry β – Δβ A/A res minimizing symmetry energy variation MD MI stiff - - soft This ratio depends only on the symm. energy variation around the neck density It should also be studied as a function of dissipation or observables connected to the density (IMF multiplicity …) < 0 Sn112 + Sn112Sn124 + 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 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 132 Sn+ 124 Sn, 100 AMeV, b=2 fm, y (0)  0.3 3H/3He n/p asy-stiff 124 Sn+ 124 Sn, 50 AMeV, b=2 fm m* n >m* p m* n <m* p

Collective flows In-plane Out-of-plane  1 < V 2 < +1 X Z y = rapidity p t = transverse momentum =  1 full out V 2 = 0 spherical = + 1 full in Differential flows 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 Mass splitting: Elliptic Flow Difference 129 Xe+ 124 Sn,100AMeV 124 Xe+ 112 Sn,100AMeV m*n < m*p m*p < m*n Triton/He3 Transverse flow ratio MSU/RIA05, nucl-th/ , AIP Conf.Proc.791 (2005) 70

Phase transitions in finite systems and isospin effects

 Validate the mechanisms investigated and the conclusions drawn from the study of symmetric matter (multifragmentation)  New features: Instabilities in asymmetric systems (phase diagram)  New features: Isospin distillation Observables: isoscaling, fragment /Z at break-up, double ratios Distillation in presence of radial flow /Z vs. E kin Phase transitions in exotic systems: new effects Density Temperature τ = 100 fm/cτ = 50 fm/c The width of the spinodal zone should depend on isospin Colonna et al., PRL2002 Level 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 E sym Increased distillation out of equilibrium

Isospin distillation in presence of radial flow  Sn112 + Sn112  Sn124 + Sn124  Sn132 + Sn132 E/A = 50 MeV, b=2 fm N = Σ i N i, Z = Σ i Z i 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 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/Z fin = a(N/Z +b), N/Z s not affected by secondary decay ! Different radial flows for neutrons and protons Fragmenting source with isospin gradient N/Z of fragments vs. Ekin ! Double ratios Central collisions p n r arXiv:

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 (p t 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 E sym (consensus on E sym ~(ρ/ρ 0 ) 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 + Sn132 E/A = 50 MeV, b=2 fm N = Σ i N i, Z = Σ i Z i 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 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/Z fin = a(N/Z +b), N/Z s not affected by secondary decay ! Different radial flows for neutrons and protons Fragmenting source with isospin gradient N/Z of fragments vs. Ekin ! Double ratios Central collisions p n r

Transverse flow of light clusters: 3H vs. 3He m* n >m* p m* n <m* p 129 Xe+ 124 Sn, 100AMeV 124 Xe+ 112 Sn, 100AMeV 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

Set of coordinates p = 260 MeV/c, Δp = 10 MeV/c, t = 0 fm/c t = 100 fm/c 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°

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 ! 124 Sn + 64 Ni 35 AMeV

v_z (c) v_x (c) Distribution after secondary decay (SIMON) Sn124 + Sn124, E/A = 50 MeV/A, b = 6 fm CM V z -V x CORRELATIONS v_par

58Fe+58Fe vs. 58Ni+58Ni b=4fm 47AMeV: Freeze-out Asymmetry distributions Fe Ni Fe Ni White circles: asy-stiff Black 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 not very sensitive to E sym ? 124 Sn Carbon isotopes (primary) A Asy-soft Asy-stiff T.X.Liu et al. PRC AMeV (central coll.)

I = I in + c(E sym, t contact ) (I av – I in ), I av = (I I 112 )/2 R P = 1 – c ; R T = c - 1 Imbalance ratios If: then: 50 MeV/A35 MeV/A Larger isospin equilibration with MI (larger t contact ? ) Larger isospin equilibration with asy-soft (larger E sym) More dissipative dynamics at 35 MeV/A

124 Sn + 64 Ni 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 v tra

Au+Au 250 AMeV, b=7 fm Z=1 data M3 centrality 6<b<7.5fm Difference of n/p flows Larger effects at high momenta Triton vs. 3 He Flows? Mass splitting: Transverse Flow Difference MSU/RIA05, nucl-th/ , AIP Conf.Proc.791 (2005) 70