Probes of EOS in Heavy Ion Collisions : results from transport theories

1. Probesof EOS in HeavyIonCollisions : resultsfromtransporttheories Nuclear Structure & Astrophysical Applications July 8-12, 2013 ECT*, TRENTO Maria Colonna INFN - Laboratori Nazionali del Sud (Catania)

2. Heavy Ion Collisions: a way to create Nuclear Matter in several conditions of ρ, T, N/Z… Nuclear effective interaction Equation of State (EOS) • Self-consistent Mean Field calculations (like HF) are a powerful framework to understand the structure of medium-heavy (exotic) nuclei. Source: F.Gulminelli • Widely employed in the astrophysicalcontext • (modelization of neutron stars and supernova explosion)

3. Dynamics of many-body systems one-body Mean-field Residual interaction TDHF Average effect of the residual interaction Fluctuations

4. Dynamics of many-body systems Transition rate W Interpreted in terms of NN cross section --Ifstatisticalfluctuationslargerthan quantum ones Main ingredients: Residual interaction (2-body correlations and fluctuations) In-medium nucleon cross section Effective interaction (self consistent mean-field) see BHF

5. 1.Semi-classicalapproximation Transportequationfor the one-bodydistributionfunctionf Chomaz,Colonna, Randrup Phys. Rep. 389 (2004) Baran,Colonna,Greco, Di Toro Phys. Rep. 410, 335 (2005) (semi-classicalanalogofWignerfunction) Residual interaction: Correlations, Fluctuations k δk vrel Vlasov Boltzmann-Langevin (BL) equation Two-body Collision Integral 2 3 4 1 (1,2) (3,4) Stochastic Mean-Field (SMF) model Fluctuations are projected in coordinate space (density profile) Fluctuations in collision integral

6. 2. Molecular Dynamics approaches (AMD, ImQMD, QMD,…) A.Ono, Phys.Rev.C59,853(1999) Zhang and Li, PRC74,014602(2006) J.Aichelin, Phys.Rep.202,233(1991) stochastic NN collisions Collision integral fully stochastic, but approx. description of mean-field effects… Colonna, Ono, Rizzo, Phys. Rev..C82,054613(2010)

7. Asysoft Asystiff Effective interactions and symmetry energy The nuclear interaction, contained in the Hamiltonian H, is represented by effective interactions (Skyrme, Gogny, …) E/A (ρ) = Es(ρ) + Esym(ρ) β² The density dependence of Esym is rather controversial, since there exist effective interactions leading to a variety of shapes for Esym: β=(ρn-ρp)/ρ Symmetry energy around ρ0 Neutron skin Isovector modes Pigmy resonances g<1 Asysoft, g>1 Asystiff γ = L/(3S0) γ = 0.5 γ = 1 • Investigate the sensitivity of the reaction dynamics • to this ingredient • Put some constraints on the effective interactions • EOS

8. Low-energyreactionmechanisms: • Fusion, Deep-Inelastic, Chargeequilibration • Fragmentationmechanisms at Fermi energies • Studyof the PDR withtransporttheories

9. Low energy reaction mechanisms Fusion vs Deep Inelastic

10. 36Ar + 96Zr , E/A = 9 MeV Fusion or break-up ? Competition between reaction mechanisms: fusion vs deep-inelastic Fusion probabilities may depend on the N/Z of the reaction partners: - A mechanism to test the isovector part of the nuclear interaction Important role of fluctuations C.Rizzo et al., PRC83, 014604 (2011)

11. Competition between reaction mechanisms t = 200 fm/c t = 40 t = 100 t = 140 t = 0 36Ar + 96Zr , E/A = 9 MeV, b = 6 fm θ β2 , β3, E*~250 MeV, J ~70ћ z (fm) • Starting from t = 200-300 fm/c, solve the Langevin Equation (LE) for selected degrees of freedom: Q (quadrupole), β3 (octupole), θ, and related velocities Break-up times of the orderof 500-1000 fm/c ! Examples of trajectories Extract the fusion cross section soft stiff Break-up configurations l (ћ) Shvedov, Colonna, Di Toro, PRC 81, 054605 (2010)

12. Chargeequilibration in fusion and D.I. collisions Relative motion of neutron and proton centers of mass TDHF calculations If N1/Z1≠ N2/Z2 Simenel et al, PRC 76, 024609 (2007) SMF simulations A1 A2 132Sn + 58Ni , D0 = 45 fm E/A = 10 MeV 40Ca + 100Mo Initial Dipole D(t) : bremss. dipole radiationCN: stat. GDR C.Rizzo et al., PRC 83, 014604 (2011)

13. 36Ar + 96Zr 40Ar + 92Zr Dynamicaldipoleemission Bremsstrahlung: Quantitative estimation V.Baran, D.M.Brink, M.Colonna, M.Di Toro, PRL.87 (2001) Experimental evidence of the extra-yield (LNS data) B.Martin et al., PLB 664 (2008) 47 Asysoft larger symmetry energy, larger effect (30 %) stiff soft soft stiff C.Rizzo et al., PRC83, 014604 (2011) see also A.Corsi et al., PLB 679, 197 (2009), LNL experiments D.Pierroutsakou et al., PRC80, 024612 (2009)

14. 1(PLF) 2(TLF) Ediss / Ecm Chargeequilibration in D.I. collisions at ~ 30 MeV/A low energy Full N/Z equilibrationnotreached: Degreeofeq. ruledbycontacttime and symmetryenergy --Chargeequilibration: fromdipoleoscillationstodiffusion Overdamped dipole oscillation D(t) Observable: (N/Z)CP = N/Z of light chargeparticles emittedby PLF as a functionof Dissipatedenergy: (impact parameter, contacttime) τd Esym t INDRA data, Galichet et al., PRC (2010)

15. “Isospindiffusion” in D.I. collisions Mass(A) ~ Mass(B) ; N/Z(A) = N/Z(B) (TLF) A dominance Isospin transport ratio R : +1 B (PLF) mixing 0 A -1 B. Tsang et al., PRL 102 (2009) B dominance -- AA and BB refer to two symmetric reactions between n-rich and n-poor nuclei AB to the mixed reaction -- X is an observable related to the N/Z of PLF (or TLF) X = N/ZPLF X = Y(7Li)/ Y(7Be) stiff soft • More centralcollisions: • largercontacttime • more dissipation, smaller R • GoodsensitivitytoAsy-EoS ComparisonbetweenImQMDcalculations and MSU data SMF calculations, 124Sn +112Sn, 50 AMeV B. Tsang et al., PRL 102 (2009) J. Rizzo et al., NPA(2008)

16. “Exotic” fragments in reactions at Fermi energies

17. PLF Fragmentationmechanisms at Fermi energies TLF Y.Zhang et al., PRC(2011) dynamicalemission IMF 124Sn + 64Ni 35 AMeV: 4π CHIMERA detector • Fragmentemission at mid-rapidity • (neckemission) • neutron-enrichmentof the neckregion Charge Z E. De Filippo et al., PRC(2012)

18. b = 6 fm, 50 AMeV PLF, TLF neck emitted nucleons asy-soft asy-stiff Sn112 + Sn112 Sn124 + Sn124 Isospin migration in neck fragmentation • Transfer of asymmetry from PLF and TLF to • the low density neck region: neutron enrichment • of the neck region • Effect related to the derivative of the symmetry • energy with respect to density Asymmetry flux ρIMF < ρPLF(TLF) stiff - full Density gradients derivative of Esym J.Rizzo et al. NPA806 (2008) 79 Larger derivative withasy-stiff largerisospinmigrationeffects The asymmetry of the neck is larger than the asymmetry of PLF (TLF) in the stiff case

19. Comparison with Chimera data Properties of ‘dynamically emitted’ (DE) fragments Charge distribution Parallel velocity distribution Good reproduction of overall dynamics The N/Z content of IMF’s in better reproduced by asystiff (L =75 MeV) DE 124Sn + 64Ni 35 AMeV SE E. De Filippo et al., PRC(2012)

20. “Exotic” collective excitations in Nuclei

21. The IsovectorDipoleResponse (DR) in neutron-rich nuclei Pygmy dipole strength • Giant DR • Pygmy DR X neutrons – protons Xc core neutrons-protons Y excess neutrons - core Klimkiewicz et al. X.Roca-Maza et al., PRC 85(2012) Isovector dipole response GDR Neutron center of mass Proton center of mass PDR

22. 132Sn • Pygmy-like initial conditions (Y) Baran et al. X Y X c Neutronskin and core are coupled The low- energyresponseisnot sensitive to the asy-stiffness -- soft --stiff --superstiff see M.Urban, PRC85, 034322 (2012) 25.0

23. GDR-like initial conditions (X) Fourier transform of D Strength of the Dipole Response E (MeV) PDR is isoscalar-like frequency not dependent on Esym GDR is isovector-like dependent on Esym The strength in the PDR region depends on the asy-stiffness (increases with L) Larger L larger strength , but also Larger L larger neutron skin 2.7 % soft 4.4 % stiff 4.5 % superstiff see A.Carbone et al., PRC 81 (2010)

24. PDR energy and strength (a systematicstudy) superstiff stiff soft Neutronskinextensionwith soft, stiff and superstiff The energycentroidof the PDR as a functionof the mass forSnisotopes, 48Ca, 68Ni, 86Kr, 208Pb ~ 41 A-1/3 superstiff stiff Correlationbetween the EWSR exhaustedby the PDR and the neutronskinextension soft V.Baran et al., arXiv:1306.4969

25. Asysoft Asystiff “Summary” of Esym constraints • Reduce experimental error bars • Perform more complete analyses • Improve theoretical description • (overcome problems related to • model dependence) Isospin diffusion Galichet 2010 De Filippo 2012 A.Carbone et al., PRC 81 (2010) V.Baran (NIPNE HH,Bucharest) M.Di Toro, C.Rizzo, J.Rizzo, (LNS, Catania) M.Zielinska-Pfabe (Smith College) H.H.Wolter (Munich) E.Galichet, P.Napolitani (IPN, Orsay)

26. Heavy Ion Collisions (HIC) allow one to explore the behavior of nuclear matter under several conditions of density, temperature, spin, isospin, … HIC from low to Fermi energies (~10-60 MeV/A) are a way to probe the density domain just around and below normal density. The reaction dynamics is largely affected by surface effects, at the borderline with nuclear structure. Increasing the beam energy, high density regions become accessible. Varying the N/Z of the colliding nuclei (up to exotic systems) , it becomes possible to test the isovector part of the nuclear interaction (symmetry energy) around and below normal density.

27. “Summary” of Esym constraints M.B.Tsang et al., PRC (2012) A.Carbone et al., PRC 81 (2010) V.Baran (NIPNE HH,Bucharest) M.Di Toro, C.Rizzo, J.Rizzo, (LNS, Catania) M.Zielinska-Pfabe (Smith College) H.H.Wolter (Munich) E.Galichet, P.Napolitani (IPN, Orsay)

28. Data: • open points higher than full points (n-rich mid-rapidity particles) • Isospin equilibration reached for Ediss/Ecm = 0.7-0.8 ? (open and full dots converge) • Data fall between the two calculations SMF transport calculations: N/Z of the PLF (Quasi-Projectile) Squares: soft Stars: stiff After statistical decay : N = Σi Ni ,Z = Σi Zi Charged particles: Z=1-4 Comparison with data -- stiff (γ=1) + SIMON forward PLF -- soft(γ=0.6) + SIMON forward n-n c.m. PLF PLF CP CP N/ZCP PLF PLF CP CP Calculations:- N/Z increases with the centrality of collision for the two systems and energies (For Ni + Ni pre-equilibrium effects) • In Ni + Au systems more isospin diffusion for asy-soft (as expected) • - (N/Z)CP linearly correlated to (N/Z)QP

29. Interpretation in termsofisovector-like and • isoscalar-likemodes in asymmetricsystems Energy-density variation Curvature matrixNormalmodes stiff soft Isoscalar-like Isovector-like α =450 for symmetric matter Zero temperature αincreaseswith L strength in the PDR region (isoscalar-like mode) increaseswith L

30. nuclearmatter in a box Fragment isotopic distribution and symmetry energy Fragmentation can beassociatedwithmean-fieldinstabilities (growthofunstablecollectivemodes) Oscillationsof the total (isoscalar-like density) fragmentformation and average Z/A (seeδρn /δρp) Oscillationsof the isovector density (ρn - ρp )isotopicvariance and distributions (Y2 / Y1 , isoscaling) Studyofisovectorfluctuations, link withsymmetryenergy in fragmentation λ = 2π/k stiff soft At equilibrium, according to the fluctuation-dissipation theorem Fv coincides with the free symmetry energy at the considered density Isovector density ρv =ρn –ρp What does really happen in fragmentation ?

31. Nuclearmatter in a box Full SMF simulations freeze-out T = 3 MeV, Density: ρ1 = 0.025 fm-3 , 2ρ1 , 3ρ1 I = 0.14 T F’ ~ T / σ Average Z/A and isovectorfluctuations as a functionoflocal density ρ M.Colonna, PRL,110(2013) ρ ρ soft stiff stiff The isospindistillation effectgoestogetherwith the isovectorvariance soft F’ follows the localequilibriumvalue ! I high density low density

32. Dissipation and fragmentation in “MD” models ImQMDcalculations, 112Sn +112Sn, 50 AMeV • More ‘explosive’ dynamics: • more fragments and • light clusters emitted • more ‘transparency’ Y.Zhang et al., PRC(2011) 124Sn +112Sn, 50 AMeV Isospin transport ratio R • Whathappenstochargeequilibration ? • Ratherflatbehaviorwith impact parameter b: • - Weakdependence on bofreactiondynamics ? • Otherdissipationsources (notnucleonexchange) ? • fluctuations, cluster emissionweaknucleonexchange

33. ComparisonSMF-ImQMD SMF = dashedlines ImQMD = full lines 6 fm γ = 0.5 8 fm • Forsemi-central impact parameters: • Largertransparencyin ImQMD(butnot so a drasticeffect) • Othersourcesofdissipation(in additiontonucleonexchange) • More cluster emission • Isospintransport R around PLF rapidity: • Good agreement in peripheralreactions • Elsewhere the differentdynamics • (nucleonexchangelessimportant in ImQMD) • leadstolessiso-equilibration γ = 2 SMF ImQMD γ = 0.5 What about fragment N/Z ? Differenttrends in ImQMD and SMF!

34. 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)