1. Maria Colonna Laboratori Nazionali del Sud (Catania) Extracting the symmetry energy from low Extracting the symmetry energy from low and medium energy heavy ion reactions LEA COLLIGA workshop October 13-15, LNS (Catania)

2. Contents Nuclear dynamics at low and Fermi energies: trying to pin down the low-density behavior of the symmetry energy Nuclear structure Nuclear astrophysics Collective excitations in exotic systems (pre-equilibrium dipole) Charge equilibration in semi-central collisions Competition between reaction mechanisms Neck dynamics Fazia Physics Case

3. Dissipative dynamics: testing the symmetry energy E sym in terrestrial laboratories currents diffusion DiffusionDrift Direct Access to Value and Slope of the Symmetry Energy at ρ ! E/A (ρ) = E s (ρ) + E sym (ρ)I ² Nuclear EOS drift coefficients Reactions at low energies: information on the EOS below normal density I=(N-Z)/A asy-soft asy-stiff Transport theories: Stochastic Mean Field (SMF) Simple hydro picture

4. D(t) : bremss. dipole radiation CN: stat. GDRInitial Dipole Pre-equilibrium Dipole Radiation Charge Equilibration Dynamics: Stochastic → Diffusion vs. Collective → Dipole Oscillations of the Di-nuclear System Fusion Dynamics - Isovector Restoring Force - Neutron emission - Neck Dynamics (Mass Asymmetry) - Anisotropy - Cooling on the way to Fusion Symmetry energy below saturation 36 Ar + 96 Zr 40 Ar + 92 Zr B.Martin et al., PLB 664 (2008) 47 Experimental evidence of the extra-yield LNS data

5. Isospin gradients: Pre-equilibrium dipole emission SPIRALS → Collective Oscillations! Bremsstrahlung: Quantitative estimations V.Baran, D.M.Brink, M.Colonna, M.Di Toro, PRL.87(2001) TDHF: C.Simenel, Ph.Chomaz, G.de France 132Sn + 58Ni124Sn + 58Ni Larger restoring force with asy-soft larger strength !

6. Rotation on the Reaction Plane of the Emitting Dinuclear System ΔΦ=2  → x=0 → a 2 =-1/4 : Statistical result, Collective Prolate on the Reaction Plane ΔΦ=0 → Φ i =Φ f = Φ 0 No rotation: Φ 0 =0 → sin 2 θ γ pure dipole ΦiΦi ΦfΦf Dynamical-dipole emission Charge equilibrium Beam Axis θ γ : photon angle vs beam axis 36Ar+96Zr vs. 40Ar+92Zr: 16AMeV Fusion events: same CN selection Angular distribution of the extra-yield (prompt dipole): anisotropy ! Accurate Angular Distrib. Measure: Dipole Clock! B.Martin et al., PLB 664 (2008) 47

7. b=8fm b=10fm M : 124 Sn + 112 Sn H: 124 Sn + 124 Sn L: 112 Sn + 112 Sn @ 35, 50 Mev/A R = ± 1 Full transparency R = 0 Full equilibration Smaller R values for: Asy-soft MI interaction Lower beam energy 50 AMeV 35 AMeV I = (N-Z)/A of PLF or TLF B. Tsang et al. PRL 92 (2004) Isospin equilibration: Imbalance ratios SMF simulations J.Rizzo et al. NPA806 (2008) 79 Phys.Rep.410(2005)335 Phys. Rep. 389 (2004)

8. Imbalance ratios: isoscalar vs. isovector effects If: β = I = (N-Z)/A τ symmetry energy t contact dissipation Kinetic energy loss - or PLF(TLF) velocity - as a measure of dissipation (time of contact) R dependent only on the isovector part of the interaction ! Overdamped dipole oscillation asy-stiff asy-soft E.Galichet INDRA collaboration

9. asy-soft asy-stiff More dissipative neck dynamics with asy-stiff ! Observables: - Deflection (Wilczynski plots) - Fragment Deformations M.Colonna, V.Baran et al., Spiral2 LOI Oct.2006 Neck Dynamics in Deep-Inelastic-Collisions Sn + Ni E lab = 10 MeV/A b = 7 fm, 9 events at t = 500 fm/c Stochastic Mean Field simulations 64 132

10. E lab = 30 Mev/A, b = 4 fm a) -- soft b) -- stiff Competition between reaction mechanisms: fusion vs deep-inelastic M.Colonna et al., PRC57(1998)1410 neutron-rich proton-rich Asy-soft more dissipative Asy-stiff more dissipative faster proton emission Opposite results with respect to simulations at lower energy !

11. Stochastic Mean Field simulations: 132Sn + 64Ni E lab = 10 MeV/A Binary events at freeze-out (≈500fm/c): Largest deformation of the residues b=6fm b=7fm b=8fm Asysoft Asystiff quadrupole octupole Asystiff: - larger residue deformations (more fast fission events) 200 runs each per impact parameter, b=6,7,8fm NN06, Rio de Janeiro NPA 787 (2007) 585c

12. Sn112 + Sn112 Sn124 + Sn124 b = 6 fm, 50 AMeV 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 Density gradients derivative of E sym E.De Filippo et al., PRC71,044602 (2005) E.De Filippo et al. NUFRA 2007 Experimental evidence of n-enrichment of the neck: Correlations between N/Z and deviation from Viola systematics LNS data – CHIMERA coll. Vrel/V Viola (IMF/PLF) (IMF/TLF) J.Rizzo et al. NPA806 (2008) 79

13. Conclusions Dissipative dynamics at Fermi energies may allow to access new, complementary information on the low density behavior of E sym  Pre-equilibrium dipole: access low-density Esym neutron skin Cooling mechanism super-heavy formation Isospin transport: Full charge equilibration at low energies ?  Neck dynamics: investigate the properties of the low-density interface  Sensitivity to detail of nuclear interaction: information on the nuclear force V.Baran (NIPNE HH,Bucharest) M.Di Toro, C.Rizzo, J.Rizzo (LNS-Catania) M.Zielinska-Pfabe (Smith College) H.H.Wolter (Munich)

14. N/Z vs charge 1200 events for each reaction  Proton/neutron repulsion: larger negative slope in the stiff case (lower symmetry energy)  n-rich clusters emitted at larger energy in n-rich systems N/Z vs fragment energy (1)  Sn112 + Sn112  Sn124 + Sn124  Sn132 + Sn132 E/A = 50 MeV, b=2 fm “gas” phase (pre-equilibrium) asy-stiff asy-soft “liquid” N = Σ i N i, Z = Σ i Z i 1.64 3≤ Zi ≤ 10 asy-stiff - - -asy-soft

15. 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 (DR) Central collisions p n r arXiv:0707.3416 DR = (N/Z) 2 / (N/Z) 1

16. 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

17. 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°

18. 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

19. 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

20. 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

21. Liquid phase: ρ > 1/5 ρ 0 Neighbouring cells are connected (coalescence procedure) Extract random A nucleons among test particle distribution Coalescence procedure Check energy and momentum conservation A.Bonasera et al, PLB244, 169 (1990) Fragment excitation energy evaluated by subtracting Fermi motion (local density approx) from Kinetic energy 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 Is it possible to reconstruct fragments and calculate their properties only from f ?  Several aspects of multifragmentation in central and semi-peripheral collisions well reproduced by the model  Statistical analysis of the fragmentation path  Comparison with AMD results Chomaz,Colonna, Randrup Phys. Rep. 389 (2004) 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) i PRC76, 024602 (2007) Rizzo, Colonna, Ono, PRC 76, 024611 (2007) Details of SMF model T ρ liquid gas Fragment Recognition

22. 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.

23. 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 2004 50 AMeV (central coll.)

24. I = I in + c(E sym, t contact ) (I av – I in ), I av = (I 124 + 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

25. 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

26. 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/0505013, AIP Conf.Proc.791 (2005) 70