Representation of a complex Green function on a real basis: Generalization to a three-body system

Abstract

We develop further a new method for employing a set of real basis functions to represent the Green function at energies in the continuum, without regard for the asymptotic boundary conditions. The method is based on the analyticity of the Green function with respect to its underlying time scale. The diagonalization of large matrices is unnecessary. Although a large complex symmetric linear system of equations must be solved, this can be done with high stability and efficiency by using a generalization of the Cholesky decomposition of real positive definite symmetric matrices. We present results of test applications to ${}^{1}$S-wave electron scattering from a hydrogen atom and photodetachment of the negative hydrogen ion. The extension from two- to three-body collisions entails the use of projection operators to distinguish different groups of asymptotic channels.