Semi-classical approaches to the phase space evolutions in intermediate energy heavy ion collisions

Abstract

The properties of semi-classical phase space evolution equations — as the Vlasov/Boltzman equations — are discussed in the context of the heavy ion reaction theory at intermediate energies (from 10 to 100 MeV per nucleon). The generalized coherent state set is shown to form a (over) complete basis for the phase space ; then every solution of the Vlasov/Boltzmann equations can be defined as a convolution product of the generalized coherent state basis by an appropriate weight function w. The uniform approximation for w is shown to provide an accurate semi-classical description of fermion systems in their ground state : the examples of fermions in a harmonic well and of cold nuclei are discussed. The solution of the Vlasov equation amounts to follow the time evolution of the coherent states which play the rôle of a moving basis. For the Boltzmann equation, the collision term is taken into account by explicit or implicit variations of the function w. Typical applications are discussed : nuclear response to the giant monopole resonance excitation, fast nucleon emission in heavy-ion reactions.