Exact distorted-wave approach to multiple-scattering theory for general potentials

TL;DR

This paper introduces an exact real-space multiple-scattering method for molecules and clusters using a distorted-wave formalism, enabling precise solutions for scattering and bound states with new Green-function re-expansion formulas.

Contribution

It develops a novel approach based on the two-potential Lippmann-Schwinger equation, deriving new Green-function formulas and secular equations for general potentials in multiple-scattering theory.

Findings

Exact solutions for scattering problems with general potentials.

New Green-function re-expansion formulas for multicenter systems.

Secular equations similar to existing methods but with improved formalism.

Abstract

We present a new approach to real-space multiple-scattering theory for molecules and clusters, based on the two-potential (distorted-wave) Lippmann-Schwinger equation formalism. Our approach uses a recently developed form [D. L. Foulis, Phys. Rev. A70, 022706 (2004)], for the partial-wave expansions of the exact time-independent single-particle Green function for a general potential, to solve exactly the scattering problem for the distorting potential. The multiple-scattering problem for the full multicenter molecular potential is then developed along familiar lines, within a partition of space consisting of non-overlapping atomic spheres, but relative to the distorting potential. To achieve this some new general Green-function re-expansion formulas are derived, as well as further developments of our earlier partial-wave expansions. Based on the division of the multicenter molecular potential into the non-singular distorting potential and a remaining singular part we develop explicitly the secular equations of our approach and prove a result concerning the symmetry of the atomic matrices. The new secular equations are similar in overall form to those of related methods, requiring coupled radial Schr\"odinger-equation solutions for each atomic center, together with atomic-sphere surface integrals, but no volume integrals. We treat both continuum (scattering) states and bound states within the same framework, and consider also the case of an outer sphere.