The incorporation of particle collisions in the time-dependent hartree-fock approximation

Abstract

In the time-dependent Hartree-Fock (TDHF) approximation, particles interact only through the mean field, and the collisions between particles are not included. Previously, we formulated the extended time-dependent Hartree-Fock (ETDHF) approximation to include particle collisions in terms of a temporal variation of the occupation probability nγ for the single-particle states. In the simplest approximation, the single-particle potential is modified only through the particle density which depends on nγ. We wish to refine the extended TDHF approximation by studying how particle collisions affect the single-particle potential. We find that it acquires two second-order contributions which are state-dependent and are the generalization of the “core polarization” and “correlation” contributions one encounters in the study of the nucleon-nucleus optical potentials. In consequence, concepts such as energy-dependent single-particle potentials and effective masses may be properly introduced in the extended TDHF approximation. We also wish to review the conservation of energy in the ETDHF approximation. We find that the total energy should include a second-order contribution due to correlations arising from particle collisions. The proper choice of single-particle basis states in the extended TDHF approximation is also discussed.