Semi-classical dynamics of heavy-ion reactions

We present a semi-classical approach of the heavy-ion collision theory in the intermediate energy domain (10-100 MeV incident kinetic energy per nucleon) based on the Vlasov equation and its extension — the Landau-Vlasov equation — when the residual interaction is accounted for through a collision kernel. We use the coherent state set as an overcomplete basis for the decomposition of the nuclear phase-space distributions. We show that the uniform repartition of coherent states in phase space provides semi-classical descriptions of nuclei at equilibrium which are the correct initial conditions of the Vlasov and Landau-Vlasov dynamical equations. In the slab geometry, we compare the results of the Vlasov equation with those of the TDHF theory for the crossing of a potential barrier and the collision of two slabs. We present sample results of three-dimensional calculations of heavy-ion collisions with a Skyrme self-consistent interaction and inclusion of the Coulomb interaction; the individual collisions being described by the Uehling-Uhlenbeck kernel. These calculations illustrate the incomplete fusion process for central collisions at 27 MeV/u incident energy and the onset of an abrasion-like process for more peripheral collisions at 35 MeV/u.