Analytical and numerical procedures in the application of many-body green's function methods to electron-atom scattering problems

Abstract

The analytical and numerical procedures used in calculation of e −-He elastic scattering phase shifts in the Generalized Random Phase Approximation (GRPA) and e −-He inelastic cross sections in the Random Phase Approximation (RPA) are presented. The pertinent equations are first written in general form and analyzed into spin and angular momentum variables. In both elastic and inelastic work the transition density matrix was represented on a basis. Finite basis sets were also used to construct the static-exchange and polarization parts of the optical potential. The elastic scattering phase shifts were then evaluated numerically. In the inelastic work all calculations were done numerically. As an illustration of the usefulness of these methods, some typical results and computational times are given.