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Probing the nuclear EOS with fragment production

Probing the nuclear EOS with fragment production. Maria Colonna Laboratori Nazionali del Sud (Catania ). Fragmentation events: IMF properties in central and semi - peripheral collisions (neutron-rich systems) Kinematical properties Size and asymmetry (N/Z)

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Probing the nuclear EOS with fragment production

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  1. Probing the nuclear EOS with fragment production Maria Colonna Laboratori Nazionali del Sud (Catania)

  2. Fragmentation events: IMF properties in central and semi-peripheral collisions (neutron-rich systems) • Kinematical properties • Size and asymmetry (N/Z) • Insight into the reaction mechanism responsible for • fragment emission and isospin transport: • density vs N/Z concentration gradients • Dependence of the results on the asy – EOS • A new method to incorporate full fluctuations into a transport treatment (Boltzmann-Langevin theory) • Conclusions and perspectives

  3. Time evolution of the one-body distribution function Vlasov Boltzmann Langevin Loss term Instantaneous equilibrium Semi-classical approach to the many-body problem Vlasov Boltzmann Langevin Vlasov: mean field Boltzmann: average collision term Langevin: randomwalk in phase-space D(p,p’,r) Ensemble average Correlation function Focus on the variance σ2f =<δfδf>

  4. Stochastic mean field (SMF) calculations (fluctuations projected on ordinary space) b = 4 fm b = 6 fm Central collisions Ni + Au, E/A = 45 MeV/A Chomaz,Colonna, Randrup Phys. Rep. 389 (2004) Sn124 + Sn124, E/A = 50 MeV/A

  5. Isospin Transport and Chemical Potentials E/A (ρ) = Es(ρ) + Esym(ρ)I² currents I=(N-Z)/A drift asy-stiff diffusion asy-soft Diffusion Drift Direct Access to Value and Slope of the Symmetry Energy at ρ!

  6. IMF properties in central collisions Sn124 + Sn124, E/A = 50 MeV/A, b = 2 fm • bubble-like configuration • radial flow • correlations:Size, N/Z vs • radial distance - velocity Primary fragment properties X.T.Liu et al, PRC69(2004) V.Baran et al, NPA703(2002)

  7. Sn112 + Sn112 • Sn124 + Sn124 • Sn132 + Sn132 E/A = 50 MeV, b=2 fm Δ Δ’ Double ratio = (N/Z)2/(N/Z)1 asy-soft asy-stiff N/Z vs fragment energy (1) N = Σi Ni ,Z = Σi Zi 3≤ Zi ≤ 10 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 (Δ’>Δ) asy-stiff asy-soft

  8. Δ Δ’ N/Z vs fragment energy (2) Double ratio R = (N/Z)2/(N/Z)1 Pre-equilibrium emission (BUU calculations) Sn124 – Sn112 IMF emission Famiano et al. PRL 06 asy-stiff asy-soft 3≤ Zi ≤ 10 IMF emission To combine the two effects: Different slope vs. n-rich cluster emission “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 Large double ratio in the asy-stiff case ! (opposite to pre-equ. emission)

  9. Original procedure by Bauer et al. • Cross section reduction • 1 nucleon = NTEST nearest neighbours • Phase-space distance • < pi > and < pj > ; Δp assigned to each “cloud” • Clouds translated to final states ( no rotation) • Pauli blocking checked only for i and j t.p. -Δp Δp J’ J p-space I I’ • Pauli violations: average trajectory altered • Shape of more similar to classical than to quantum case Fluctuations in phase space • Our improved method • test particles i and j cells I and J • Spherical search around I and J • “clouds” rotated to final states (Improve the treatment of fluctuations in p space) • Still arbitrary: • r-space distance Bauer, Bertsch, Das Gupta, PRL58 (1987) 58 • Procedure easily applicable to nuclear reactions • Careful check of Pauli-blocking • Take into account possible nucleon deformations in p space

  10. In this case: ‘nucleon’ volume Our result: Set of coordinates t =0 t = 100 fm/c t = 100 fm/c t = 0 fm/c p = 260 MeV/c, Δp = 10 MeV/c, Illustrative results Check of the <f> profile r-space: periodic 3-D box, l = 26 fm; ρ = 0.16 fm-3 (2820 nucleons); 500 test particles p-space: Fermi-Dirac configuration , kT = 5 MeV Δp Check of the fluctuation variance on the Fermi surface

  11. Propagation of fluctuations by the unstable mean-field -3 Box calculations : ρ = 0.05 fm, T = 3 MeV Fourier analysis of the density variance <δρδρ> : rapid growth of density fluctuations Fragment multiplicity and charge distributions (300 nucleons)

  12. CONCLUSIONS • Study of IMF’s emitted in heavy ion collisions: • Correlations between N/Z and velocity • Fragments with smaller kinetic energy are more neutron rich (asy – stiff) • Double ratios as sensitive observables to the asy-EOS • Development of a full 3D treatment of the BL theory : • Improvement of thetreatment of fluctuations in p space (thermal fluctuations) V.Baran (NIPNE HH,Bucharest) M.Di Toro, J. Rizzo (LNS-Catania) Ph. Chomaz (GANIL, France) H.H. Wolter (Munich)

  13. N/Z-IMF vs. Alignement Correlation in semi-peripheral collisions 124Sn + 64Ni 35 AMeV ternary events 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)

  14. 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

  15. BNV - 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)

  16. Competition between reaction mechanisms: fusion vs deep-inelastic a) soft b) stiff neutron-rich Elab = 30 Mev/A, b = 4 fm proton-rich M.Colonna et al., PRC57(1998)1410

  17. Comparison with INDRA data -- stiff -- soft forward c.m. forward QP

  18. H L H L H L H L INDRA data: Ni + Ni, Ni + Au @ 52, 74 MeV/A: N/Z vs b if I = Iin +c(Esym)(Iav – Iin) RP = 1 – c ; RT = c - 1 soft stiff 20% difference in the slope between stiff and soft E.Galichet et al., Nucl.Phys.A submitted b IPN, Orsay

  19. asy-stiff asy-soft Competition between deep-inelastic and neck emission asy-stiff More dissipative neck dynamics with asy-stiff ! 64 132 Sn + Ni Elab = 10 MeV/A b = 6,7,8 fm, t = 500 fm/c Octupole distribution asy-soft V.Baran, Aug.06 SPIRAL2 proposal

  20. Isospin effects on dissipation INDRA data: Ni + Ni, Ni + Au @ 52, 74 MeV/A soft stiff E.Galichet et al., Nucl.Phys.A submitted IPN, Orsay

  21. 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 !

  22. 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)

  23. 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

  24. 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

  25. 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

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