Noniterative solutions of integral equations for scattering. I. Single channels

Abstract

A new method (homogeneous integral solution) for solving collision problems utilizing an integral equa-tion formalism is presented. The approach is noniterative and applies equally well to purely local inter-actions or problems with combined local and nonlocal interactions. The method involves transforming the integral equation of scattering into a Volterra integral equation of the second kind. It follows that even for nonlocal interactions, the wavefunction may be determined noniteratively from knowledge of its value at a single point (the origin). A simple numerical procedure is proposed for solution of the Volterra equation which allows one to avoid matrix inversions completely. At the end of the calculation, the scattering T or R matrix is obtained directly from the solutions. The method is illustrated by a calculation of the singlet and triplet s-wave Hartree-Fock phase shifts for electron-H-atom scattering.