Reaction mechanisms in transport theories: a test of the nuclear effective interaction Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) NN TH INTERNATIONAL CONFERENCE ON NUCLEUS-NUCLEUS COLLISIONS May 27-June 1, 2012 San Antonio, Texas

 Collective excitations in neutron-rich systems  Dissipation and fragmentation mechanisms at Fermi energies

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

The nuclear interaction, contained in the Hamiltonian H, is represented by effective interactions (Skyrme, Gogny, …) E/A (ρ) = E s (ρ) + E sym (ρ) β² β=(ρ n -ρ p )/ρ The density dependence of E sym is rather controversial, since there exist effective interactions leading to a variety of shapes for E sym :  Asysoft,  Asystiff Investigate the sensitivity of the reaction dynamics to this ingredient Put some constraints on the effective interactions Symmetry energy Asysoft Asystiff Neutron skin Isovector modes Pigmy resonances around ρ 0 Effective interactions and symmetry energy γ = 2 γ = 0.5

“Exotic” collective excitations in Nuclei

Isovector dipole response PDR GDR The Isovector Dipole Response (DR) in neutron-rich nuclei The DR in 132 Sn: a study within semi-classical transport theories The neutron skin is sensitive to asy-stiffness: larger in the stiff cases X.Roca-Maza et al., PRC 85(2012) Pygmy dipole strength  Giant DR  Pygmy DR Klimkiewicz et al.

 Isovector dipole moment (L = 1) X neutrons – protons X c core neutrons-protons Y excess neutrons - core Neutron center of mass Proton center of mass The Isovector Dipole Response (DR) in neutron-rich nuclei 19.5%: too much ! Analysis of collective motion with transport theory (Vlasov)

Pygmy-like initial conditions (Y) X Y Fourier transform of D Strength of the Dipole Response X c Neutron skin and core are coupled The low- energy response is not sensitive to the asy-stiffness -- soft -- stiff -- superstiff Baran et al.

 Interpretation in terms of isovector-like and isoscalar-like modes in asymmetric systems D Pygmy-like GDR (isovector-like) PDR (isoscalar-like) θ PDR is isoscalar-like not dependent on E sym GDR is isovector-like dependent on E sym The strength in the PDR region depends on the asy-stiffness (increases with L) Larger L larger θ, but also Larger L larger neutron skin 2.7 % soft 4.4 % stiff 4.5 % superstiff A.Carbone et al., PRC 81 (2010)

Fermi energy mechanisms: Dissipation and fragmentation in Heavy Ion Collisions

 Diffusion: mass exchange, charge equilibration, energy dissipation Dissipation and fragmentation in “MF” models R SMF calculations, 124 Sn Sn, 50 AMeV Isovector modes faster than isoscalar modes: τ d /τ ex < 1 Larger symmetry energy at low density: Faster equilibration with soft (PLF) (neck)  Neck instabilities: important role of fluctuations…. but still ‘mean-field’ dominated mechanism: isospin migration soft stiff Relative weight of Is and Iv dissipation: J. Rizzo et al., NPA(2008) Isospin transport ratio

Dissipation and fragmentation in “MD” models ImQMD calculations, 112 Sn Sn, 50 AMeV  More ‘explosive’ dynamics: more fragments and light clusters emitted more ‘transparency’ What happens to charge equilibration ? Rather flat behavior with impact parameter b: - Weak dependence on b of reaction dynamics ? - Other dissipation sources (not nucleon exchange) ? fluctuations, cluster emission weak nucleon exchange Isospin transport ratio R Y.Zhang et al., PRC(2011) 124 Sn Sn, 50 AMeV

Comparison SMF-ImQMD 6 fm 8 fm γ = 0.5 SMF = dashed lines ImQMD = full lines  For semi-central impact parameters: Larger transparency in ImQMD (but not so a drastic effect) Other sources of dissipation (in addition to nucleon exchange) More cluster emission SMF ImQMD γ = 0.5 Different trends in ImQMD and SMF! What about fragment N/Z ? γ = 2  Isospin transport R around PLF rapidity : Good agreement in peripheral reactions Elsewhere the different dynamics (nucleon exchange less important in ImQMD) leads to less iso-equilibration

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 Mid-peripheral impact parameters: Results are model-dependent Important to study the reaction dynamics (dissipation and nature of dissipation) Summary  Mechanisms at Fermi energies PLF IMF’s V.Baran, B.Frecus (Bucharest), M. Di Toro (LNS) Y.Zhang (CIAE, Beijing) In collaboration with  Collective excitation in n-rich nuclei: transport theories predict a good sensitivity to asy-EoS (GDR energy) PDR is isoscalar-like, its relative strength depends on asy-EoS

Isospin transport and fragmentation mechanisms in semi-central collisions Simple hydro picture DiffusionDrift drift diffusion -- Drift: Isospin migration ρ neck < ρ PLF(TLF) Asymmetry flux -- Diffusion: charge equilibration Overdamped dipole oscillation τ d E sym t D(t) neck instabilities soft stiff β=(ρ n -ρ p )/ρ Sn112Sn124 b = 6 fm, 50 AMeV Neck fragments are neutron-richer than PLF-TLF neck PLF-TLF

B. Tsang et al. PRL 102 (2009) Mass(A) ~ Mass(B) ; N/Z(A) = N/Z(B) Isospin transport ratio R : A dominance mixing B dominance AA and BB refer to two symmetric reactions between n-rich and n-poor nuclei AB to the mixed reaction R(t) = 2(x AB (t) – x m ) / (x A – x B ) R AB = e -t/τ d τ d E sym -- X is an observable related to the N/Z of the projectile-like fragments (PLF) A B Tools to study charge equilibration between A and B x m = (x A + x B )/2 stiff soft  More central collisions: larger contact time more dissipation, smaller R  Good sensitivity to Asy-EoS SMF calculations 124 Sn Sn, 50 AMeV X = N/Z PLF t = contact time

The strength in the PDR region depends on the asy-stiffness (increases with L) Larger L larger θ, but also Larger L larger neutron skin 1) GDR-like initial conditions (X) D GDR (isovector-like) PDR (isoscalar-like) Pygmy-like GDR (isovector-like) PDR (isoscalar-like) θ 2.7 % soft 4.4 % stiff 4.5 % superstiff

Dynamics of many-body systems Mean-fieldResidual interaction Average effect of the residual interaction one-body Fluctuations TDHF

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, (2007) Rizzo, Colonna, Ono, PRC 76, (2007) Details of SMF model T ρ liquid gas Fragment Recognition