Multi-variate Bateman method for two-body scattering without partial-wave decomposition

Abstract

The use of Bateman method for solving the two-variable version of the two-body Lippmann-Schwinger equation without recourse to partial-wave decomposition is investigated. Bateman method is based on a special kind of interpolation of the momentum representation of the potential on a multi-variate grid. A suitable scheme for the generation of a multi-variate Cartesian grid is described. The method is tested on the Hartree potential for electron-hydrogen scattering in the static no-exchange approximation. Our results show that the Bateman method is capable of producing quite accurate solutions with relatively small number of grid points.