Method of continued fractions with application to atomic physics

Abstract

A new iterative method for solving scattering integral equations for local as well as nonlocal potentials is proposed. The scattering matrix is expressed in the form of a continued fraction. This method converges extremely fast for compact potentials with arbitrary strength. A high precision of the result is expected with a relatively small amount of numerical work. Starting from the second iteration, all functions which are to be computed in the course of iterations are regular at the origin and are of finite range in configuration space. The method is applied to the elastic scattering of electrons from hydrogen atoms in the static, exchange approximation. Its efficiency is compared with some recently proposed methods.