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arXiv · 0806.0574

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

D. L. Foulis
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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 Schrödinger-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.

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D. L. Foulis. 2008-06-03. Exact distorted-wave approach to multiple-scattering theory for general potentials. https://arxiv.org/abs/0806.0574

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