Equilibration in the time-dependent Hartree-Fock approach probed with the Wigner distribution function

Abstract

Calculating the Wigner distribution function in the reaction plane, we are able to probe the phase-space behavior in time-dependent Hartree-Fock during a heavy-ion collision. We compare the Wigner distribution function with the smoothed Husimi distribution function. Observables are defined to give a quantitative measure for local and global equilibration. We present different reaction scenarios by analyzing central and non-central $^{16}O+$$^{16}O$ and $^{96}Zr+$$^{132}Zn$ collisions. It is shown that the initial phase-space volumes of the fragments barely merge. The mean values of the observables are conserved in fusion reactions and indicate a "memory effect" in time-dependent Hartree-Fock. We observe strong dissipation but no evidence for complete equilibration.