Maria Colonna Laboratori Nazionali del Sud (Catania )

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

2. What can we learn from reactions at intermediate energy (30-100 MeV/A) with exotic beams ? • 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

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

4. asy-stiff asy-soft Isospin Transport: the density dependent Esym Self-consistent mean-field calculations currents E/A (ρ) = Es(ρ) + Esym(ρ)I² I=(N-Z)/A drift diffusion Diffusion Drift Direct Access to Value and Slope of the Symmetry Energy at ρ!

5. Symmetry Potentials and Effective Masses Momentum dependence Density dependence 124Sn “asymmetry” I = 0.2 Lane Potentials (Un-Up)/2I neutron proton Asy-stiff Asy-soft Phys.Rep.410(2005)335-466

6. The density-dependent symmetry energy and n-p effective mass splitting: Observables • 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 pt distribution of pre-equilibrium emission, • collective flows, light clusters • Disantangle isovector effects from isoscalar effects • Better focus on iso-EOS

7. SMF - transport model b=8fm b=9 fm b=10fm 120fm/c b=8fm 100fm/c 80fm/c b=10fm ISOSPIN DIFFUSION AT FERMI ENERGIES 124Sn + 112Sn at 50 AMeV contact time Imbalance ratios asysoft eos superasystiff eos asy-soft EOS – faster equilibration experimental data (B. Tsang et al. PRL 92 (2004) ) Baran, Colonna, Di Toro, Pfabe, Wolter, PRC72(2005)

8. Imbalance ratios: isoscalar vs. isovector effects MD, MI: isoscalar effective forces If: then: τsymmetry energy tcontact dissipation β = (N-Z)/A Kinetic energy loss as a measure of dissipation (time of contact) R dependent only on the isovector part of the interaction !

9. Density gradients derivative of Esym Asymmetry flux ρ2 ρ1 < 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 b = 6 fm, 50 AMeV PLF, TLF neck emitted nucleons asy-stiff asy-soft Larger derivative with asy-stiff larger isospin migration effects Sn112 + Sn112 Sn124 + Sn124 arXiv:0711.3761

10. ρR ρI < Isospin exchange: βIMF/ βres ratio Neck mass A, asymmetry β + Δβ Residues mass Ares, asymmetry β – Δβ A/Ares A Ares Asymmetry flux < 0 minimizing symmetry energy variation b = 6 fm, 50 AMeV 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 …) MD MI stiff - - soft Sn112 + Sn112 Sn124 + Sn124

11. Mass splitting: N/Z of Fast Nucleon Emission Gas asymmetry vs. p_t 124Sn+124Sn, 50 AMeV, b=2 fm 132Sn+124Sn, 100 AMeV, b=2 fm, y(0)0.3 n/p 3H/3He asy-stiff asy-stiff • m*n>m*p • m*n<m*p Vs. Kinetic Energies Light isobar (3H/3He) yields High p_t “gas” asymmetry: Observable very sensitive to the mass splitting and not to the asy-stiffness J.Rizzo et al., PRC 72 (2005) → Isotope Science Facility at MSU, White Paper 2006

12. = - 1 full out V2 = 0 spherical = + 1 full in Isospin Collective flows In-plane Out-of-plane y = rapidity pt = transverse momentum X Z -1 < V2 < +1 Differential flows B-A Li et al. PRL2002

13. Au+Au 250 AMeV, b=7 fm Mass splitting: Elliptic Flow Difference Z=1 data, M3 centrality, 6<b<7.5fm 129Xe+124Sn,100AMeV 124Xe+112Sn,100AMeV m*n < m*p m*p < m*n m*n<m*p : larger neutron squeeze out at mid-rapidity MSU/RIA05, nucl-th/0505013 , AIP Conf.Proc.791 (2005) 70 Triton/He3 Transverse flow ratio

14. Phase transitions in finite systems and isospin effects

15. Phase transitions in exotic systems: new 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 distillationObservables: isoscaling, fragment <N>/Z at break-up, double ratios • Distillation in presence of radial flow <N>/Z vs. Ekin τ = 100 fm/c τ = 50 fm/c The width of the spinodal zone should depend on isospin Temperature Level density, limiting temperature … Density Colonna et al., PRL2002

16. Density gradients derivative of Esym β = 0.2 β = 0.1 Isospin-dependent phase transition Isospin distillation: the liquid phase is more symmetric than the gas phase asy-stiff Increased distillation out of equilibrium asy-soft asy-stiff - - -asy-soft Spinodal decomposition in a box Non-homogeneous density F.Matera, in preparation

17. n p Isospin distillation in presence of radial flow Central collisions • Sn112 + Sn112 • Sn124 + Sn124 • Sn132 + Sn132 E/A = 50 MeV, b=2 fm Different radial flows for neutrons and protons Fragmenting source with isospin gradient N/Z of fragments vs. Ekin ! r N = Σi Ni ,Z = Σi Zi 3≤ Zi ≤ 10 asy-stiff - - -asy-soft Double ratios 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 ! • Proton/neutron repulsion: • larger negative slope in the stiff case (lower symmetry energy) • n-rich clusters emitted at larger • energy in n-rich systems arXiv:0707.3416

18. 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.

19. Conclusions and Perspectives -II- • 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 γ V.Baran (NIPNE HH,Bucharest) M.Di Toro, J. Rizzo (LNS-Catania) F. Matera (Florence) M. Zielinska-Pfabe (Smith College) H.H. Wolter (Munich)

20. n p Isospin distillation in presence of radial flow Central collisions • Sn112 + Sn112 • Sn124 + Sn124 • Sn132 + Sn132 E/A = 50 MeV, b=2 fm Different radial flows for neutrons and protons Fragmenting source with isospin gradient N/Z of fragments vs. Ekin ! r N = Σi Ni ,Z = Σi Zi 3≤ Zi ≤ 10 asy-stiff - - -asy-soft Double ratios 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 ! • Proton/neutron repulsion: • larger negative slope in the stiff case (lower symmetry energy) • n-rich clusters emitted at larger • energy in n-rich systems

21. 129Xe+124Sn, 100AMeV 124Xe+112Sn, 100AMeV Transverse flow of light clusters: 3H vs. 3He Larger 3He flow (triangles) Coulomb effects Larger difference for m*n>m*p m*n>m*p m*n<m*p Triton/Helium transverse flow ratio: smaller for m*n>m*p Good sensitivity to the mass splitting

22. The variance of the distribution function Best volume: p = 190 MeV/c, θ = 20° p = 190 MeV/c Δθ = 30° Set of coordinates Clouds position t = 100 fm/c t = 0 fm/c p = 260 MeV/c, Δp = 10 MeV/c, • spherical coordinates • fit the Fermi sphere • allow large volumes

23. DEVIATIONSFROMVIOLASYSTEMATICS r - ratio of the observed PLF-IMFrelative velocityto the corresponding Coulombvelocity; r1- the same ratio for the pair TLF-IMF TheIMF is weakly correlated with both PLF and TLF 124Sn + 64Ni 35 AMeV Wilczynski-2 plot !

24. CM Vz-Vx CORRELATIONS v_par Sn124 + Sn124, E/A = 50 MeV/A, b = 6 fm v_x (c) Distribution after secondary decay (SIMON) v_z (c)

25. 58Fe+58Fe vs. 58Ni+58Ni b=4fm 47AMeV: Freeze-out Asymmetry distributions Fe Ni Ni Fe White circles: asy-stiff Black circles: asy-soft Fe: fast neutron emission Ni: fast proton emission Asy-soft: small isospin migration

26. 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 PLF-IMF to TLF and the direction defined by the relative velocity of PLF to IMF

27. Dynamical Isoscaling Z=1 Z=7 Asy-stiff Asy-soft A primary 50 AMeV (central coll.) final not very sensitive to Esym ? 124Sn Carbon isotopes (primary) T.X.Liu et al. PRC 2004

28. 50 MeV/A 35 MeV/A Imbalance ratios If: I = Iin +c(Esym, tcontact)(Iav – Iin), Iav = (I124 + I112)/2 then: RP = 1 – c ; RT = c - 1 • Larger isospin equilibration with MI • (larger tcontact ? ) • Larger isospin equilibration with asy-soft • (larger Esym) • More dissipative dynamics at 35 MeV/A

29. N/Z vs. Alignement Correlation in semi-peripheral collisions vtra 124Sn + 64Ni 35 AMeV ternary events φ Transp. Simulations (124/64) Experiment Histogram: no selection Asystiff Asysoft Asystiff: more isospin migration to the neck fragments Chimera data: see E.De Filippo, P.Russotto NN2006 Contr., Rio V.Baran, Aug.06 E.De Filippo et al. , PRC71(2005)

30. Au+Au 250 AMeV, b=7 fm Mass splitting: Transverse Flow Difference Difference of n/p flows Larger effects at high momenta Z=1 data M3 centrality 6<b<7.5fm Triton vs. 3He Flows? MSU/RIA05, nucl-th/0505013 , AIP Conf.Proc.791 (2005) 70