Approximate Formula for Scattering Matrix in Many-State Collision Problem: Extension of the BII Approximation

Abstract

By dealing with the system of the coupled radial Schroedinger equations, many-state collision problem is investigated theoretically. Replacing the Green operators of the radial differential Schroedinger operators by their δ-function parts, we can treat the problem successfully with some allowance foe effects of all coupling potentials. The method employed in the author’s previous papers is used to treat the non-local complex potentials. As a demonstration a three-state case is considered and a new approximate formula for scattering matrix is derived. In a certain limiting case the formula obtained reduces to a corresponding one in the BII approximation proposed by Seaton for electron-atom collisions. This formula will be applicable to a wide class of collision processes.