The Multidimensional Angular Coulomb Function Method in Atomic and Molecular Physics

Abstract

I. At the last time a certain progress has been achieved in developing unified approaches to studying few-body properties based on non-model solutions of problems of discrete and continuous spectrum. The hyperspherical function method and its versions in the quark model of elementary particles, multinucleon theory of nuclei, atomic physics and quantum chemistry are enough widely spread [1, 2, 3]. However the hyperspherisal functions, used in the MHCF, being solutions of multidimensional Laplace equation, are a subset of wider set of multidimensional angular functions (MAF). In general case, the MAF may be constructed in multidimensional spaces with several collective variables determined so to describe prevailing motions in multipartial systems. New opportunities are opened with using methods of MAF, which may not be the characteristic functions of Laplace operator, what require calculating matrix elements of kinetic energy operator by the MAF. In the report we consider one of indicated total bases of MAF allowing for the most full specifics of multipartial problems with long-range Coulomb interaction, which received the name method of multidimensional angular Coulomb functions (MACF).