Reaction mechanisms in transport theories : a test of the nuclear effective interaction

1. Reactionmechanisms in transporttheories: a test of the nucleareffectiveinteraction NN2012 11TH INTERNATIONAL CONFERENCE ON NUCLEUS-NUCLEUS COLLISIONS May 27-June 1, 2012 San Antonio, Texas Maria Colonna INFN - Laboratori Nazionali del Sud (Catania)

2. Collectiveexcitations in neutron-richsystems • Dissipation and fragmentationmechanisms • at Fermi energies

3. Semi-classicalapproximation Transportequationfor the one-bodydistributionfunctionf Chomaz,Colonna, Randrup Phys. Rep. 389 (2004) Baran,Colonna,Greco, Di Toro Phys. Rep. 410, 335 (2005) Residual interaction: Correlations, Fluctuations k δk Two-body Collision Integral Effective interactions EDF theories: The exact density functional is approximated with powers and gradients of one-body nucleon densities and currents. (1,2) (3,4) Fluctuations in collision integral Stochastic Mean-Field (SMF) model Mean-field effects well described, but fluctuations underestimated…

4. 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 Neutron skin Isovector modes Pigmy resonances around ρ0 g<1 Asysoft, g>1 Asystiff γ = 0.5 • Investigate the sensitivity of the reaction dynamics • to this ingredient • Put some constraints on the effective interactions γ = 2

5. “Exotic” collectiveexcitations in Nuclei

6. The IsovectorDipoleResponse (DR) in neutron-rich nuclei Pygmydipolestrength • Giant DR • Pygmy DR Klimkiewiczet al. X.Roca-Mazaet al., PRC 85(2012) Isovectordipoleresponse The DR in 132Sn: a studywithinsemi-classicaltransporttheories GDR The neutronskinis sensitive toasy-stiffness: larger in the stiffcases PDR

7. The IsovectorDipoleResponse (DR) in neutron-rich nuclei • Isovectordipole moment (L = 1) X neutrons – protons Xccoreneutrons-protons Y excessneutrons - core Neutron center of mass Proton center of mass 19.5%: toomuch ! Analysisofcollectivemotionwithtransporttheory (Vlasov)

8. Pygmy-likeinitialconditions (Y) Baranet al. X Y X c Neutronskin and core are coupled The low- energyresponseisnot sensitive to the asy-stiffness -- soft --stiff --superstiff Fourier transformof D Strengthof the DipoleResponse

9. Interpretation in termsofisovector-like and • isoscalar-likemodes in asymmetricsystems θ Pygmy-like D GDR (isovector-like) PDR isisoscalar-likenotdependent on Esym GDR isisovector-likedependent on Esym PDR (isoscalar-like) The strength in the PDR regiondepends on the asy-stiffness (increaseswith L) Larger L largerθ, butalso Larger L largerneutronskin 2.7 % soft 4.4 % stiff 4.5 % superstiff A.Carboneet al., PRC 81 (2010)

10. Fermi energymechanisms: Dissipation and fragmentation in HeavyIonCollisions

11. Dissipation and fragmentation in “MF” models • Diffusion: mass exchange, chargeequilibration, energydissipation Isospintransportratio Isovectormodesfasterthan isoscalarmodes: τd/τex < 1 Relative weight of Is and Iv dissipation: R Largersymmetryenergy at low density: Fasterequilibration withsoft SMF calculations, 124Sn +112Sn, 50 AMeV • Neck instabilities: important role of fluctuations…. • but still ‘mean-field’ dominated mechanism: • isospin • migration (PLF) soft (neck) stiff J. Rizzo et al., NPA(2008)

12. 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

13. 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!

14. Summary • Collectiveexcitation in n-rich nuclei: • transporttheoriespredict a goodsensitivitytoasy-EoS (GDR energy) • PDR isisoscalar-like, its relative strengthdepends on asy-EoS • Mechanisms at Fermi energies • Mid-peripheral impact parameters: Results are model-dependent • Importanttostudythe reactiondynamics(dissipation and nature ofdissipation) Look at the correlation between charge and velocity of PLF residues and IMF’s (2<Z<9) multiplicity N/Z of neck fragments can help to check the reaction dynamics Isospin as a tracer V.Baran, B.Frecus (Bucharest), M. Di Toro (LNS)Y.Zhang (CIAE, Beijing) PLF In collaborationwith IMF’s

15. Isospin transport and fragmentation mechanisms in semi-central collisions soft neckinstabilities stiff Simple hydro picture Diffusion Drift diffusion drift --Diffusion: chargeequilibration Overdamped dipole oscillation D(t) τd Esym t -- Drift: Isospin migration b = 6 fm, 50 AMeV β=(ρn-ρp)/ρ Asymmetry flux neck Neck fragments are neutron-richer than PLF-TLF PLF-TLF ρneck < ρPLF(TLF) Sn112 Sn124

16. Toolstostudychargeequilibrationbetween A and B Mass(A) ~ Mass(B) ; N/Z(A) = N/Z(B) A dominance Isospin transport ratio R : +1 B mixing 0 A R(t) = 2(xAB(t)– xm) / (xA – xB) -1 B. Tsang et al. PRL 102 (2009) B dominance RAB = e-t/τd τd Esym -- 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 the projectile-like fragments (PLF) stiff soft SMF calculations 124Sn +112Sn, 50 AMeV xm = (xA + xB)/2 t = contacttime • More centralcollisions: largercontacttime • more dissipation, smaller R • GoodsensitivitytoAsy-EoS X = N/ZPLF

17. 1) GDR-likeinitialconditions (X) θ D GDR (isovector-like) PDR (isoscalar-like) GDR (isovector-like) Pygmy-like The strength in the PDR regiondepends on the asy-stiffness (increaseswith L) Larger L largerθ, butalso Larger L largerneutronskin PDR (isoscalar-like) 2.7 % soft 4.4 % stiff 4.5 % superstiff

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

19. 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)