Integral equation method for the determination of the scattering amplitude

Abstract

An integral equation, derived from the Lippmann-Schwinger equation for the full wave function, is solved by converting it to matrix form by use of numerical quadrature. The scattering amplitude is then determined. The procedure is applied to the screened Coulomb potential. Quite good agreement with exact results is achieved with not too many quadrature points. In particular, fairly accurate total cross sections are obtained by use of the optical theorem. The numerical procedure does not, however, appear to converge rapidly to the exact results.