Time-independent mean field theory of collisions: the case of long range forces

Abstract

Instead of diagonalizing the many-body Hamiltonian H, the authors invert E-H, where E is a complex energy, which is eventually made real. All the traditional approximations to diagonalization may be adopted for the evaluation of (E-H)-1. Mean field methods are specially investigated. Previous papers reported several numerically soluble cases where a time-independent mean field approximation (TIMF) was tested with success for the calculation of collision amplitudes with short range forces. They test the validity of TIMF for a long range interaction: the Coulomb Green function for two particles is found to be successfully approximated by TIMF.