Inelastic Collisions of Slow Atoms: The Two-Level Model

Abstract

A two-level model of an atomic system is investigated in order to study the cross section for certain inelastic collision processes. An impact-parameter method is employed. The time-dependent Schrödinger equation has been integrated numerically for some simple interaction potentials. Cross sections for excitation have been determined and are presented as functions of the parameters describing the model. The results are compared with those obtained by certain approximate methods. The effects of inclusion of diagonal matrix elements in the interaction Hamiltonian are found to be large. For a fixed form of the interaction potential, two cross sections, which may differ quite substantially, are obtained, depending on the algebraic sign of the coupling parameters or the energy difference between the states.