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Maria Colonna Laboratori Nazionali del Sud (Catania )

Extracting the symmetry energy from low and medium energy heavy ion reactions. Maria Colonna Laboratori Nazionali del Sud (Catania ). L EA C OLLIGA workshop October 13-15, LNS (Catania). Nuclear astrophysics. Nuclear structure. Contents. Nuclear dynamics at low and Fermi energies:

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Maria Colonna Laboratori Nazionali del Sud (Catania )

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

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

  3. I=(N-Z)/A asy-stiff asy-soft Dissipative dynamics: testing the symmetry energy Esym in terrestrial laboratories Nuclear EOS Transport theories: Stochastic Mean Field (SMF) E/A (ρ) = Es(ρ) + Esym(ρ)I² Simple hydro picture currents drift diffusion coefficients Diffusion Drift Direct Access to Value and Slope of the Symmetry Energy at ρ! Reactions at low energies: information on the EOS below normal density

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

  5. Isospin gradients: Pre-equilibrium dipole emission SPIRALS → Collective Oscillations! TDHF: C.Simenel, Ph.Chomaz, G.de France 132Sn + 58Ni 124Sn + 58Ni Bremsstrahlung: Quantitative estimations V.Baran, D.M.Brink, M.Colonna, M.Di Toro, PRL.87(2001) Larger restoring force with asy-soft larger strength !

  6. Rotation on the Reaction Plane of the Emitting Dinuclear System Dynamical-dipole emission Charge equilibrium ΔΦ=2 → x=0 → a2=-1/4 : Statistical result, Collective Prolate on the Reaction Plane Φf Φi Beam Axis θγ: photon angle vs beam axis ΔΦ=0 → Φi =Φf = Φ0 No rotation: Φ0=0 → sin2θγpure dipole 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 Isospin equilibration: Imbalance ratios B. Tsang et al. PRL 92 (2004) M : 124Sn + 112Sn SMF simulations L: 112Sn + 112Sn Phys. Rep. 389 (2004) H: 124Sn + 124Sn Phys.Rep.410(2005)335 @ 35, 50 Mev/A I = (N-Z)/A of PLF or TLF R = ± 1 Full transparency 35 AMeV R = 0 Full equilibration • Smaller R values for: • Asy-soft • MI interaction • Lower beam energy 50 AMeV J.Rizzo et al. NPA806 (2008) 79

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

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

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

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

  12. LNS data – CHIMERA coll. Density gradients derivative of Esym Asymmetry flux (IMF/TLF) Vrel/VViola (IMF/PLF) ρ2 ρ1 < Experimental evidence of n-enrichment of the neck: Correlations between N/Z and deviation from Viola systematics 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 E.De Filippo et al., PRC71,044602 (2005) E.De Filippo et al. NUFRA 2007 Sn112 + Sn112 Sn124 + Sn124 Larger derivative with asy-stiff larger isospin migration effects 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 Esym • 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. Sn112 + Sn112 • Sn124 + Sn124 • Sn132 + Sn132 E/A = 50 MeV, b=2 fm N/Z vs fragment energy (1) N = Σi Ni ,Z = Σi Zi 3≤ Zi ≤ 10 asy-stiff - - -asy-soft 1.64 1200 events for each reaction N/Z vs charge “gas” phase (pre-equilibrium) “liquid” • Proton/neutron repulsion: • larger negative slope in the stiff case (lower symmetry energy) • n-rich clusters emitted at larger • energy in n-rich systems asy-stiff asy-soft

  15. 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 (DR) 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

  16. 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

  17. 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

  18. 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 !

  19. 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)

  20. 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

  21. Details of SMF model • Correlations are introduced in the time evolution of the one-body density: ρρ +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 ? T gas 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 Neighbouring cells are connected (coalescence procedure) Fragment Recognition 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 • 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) iPRC76, 024602 (2007) Rizzo, Colonna, Ono, PRC 76, 024611 (2007)

  22. 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

  23. 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

  24. 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

  25. 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)

  26. 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

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