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

TL;DR

This paper explores the application of the Bateman method to solve the two-body scattering problem directly in momentum space without partial-wave decomposition, demonstrating its accuracy and efficiency.

Contribution

It introduces a novel scheme for applying the Bateman method to two-variable Lippmann-Schwinger equations using a multi-variate grid, avoiding partial-wave expansion.

Findings

Accurate solutions with fewer grid points

Effective for nucleon-nucleon scattering

Potential for computational efficiency

Abstract

The use of Bateman method for solving the two-variable version of the 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 in the nucleon-nucleon scattering employing a model two-nucleon potential. Our results show that the Bateman method is capable of producing quite accurate solutions with relatively small number of grid points.