A multi-cluster, n-particle generalization of the three-particle faddeev wavefunction equations

Abstract

Recent work applying certain forms of many-body scattering theory to problems such as molecular potential energy surfaces and equations for nonequilibrium statistical mechanics indicates that a formulation of the theory based directly on multi-cluster, n-particle, wave function components could be of some utility. Such a formulation is derived in this paper using techniques from the Baer-Kouri-Levin-Tobocman and Bencze-Redish-Sloan-Polyzou theories of multi-particle scattering. It is based on components corresponding to the various multi-cluster partitions of an n-particle scattering system and is a generalization of the three-body Faddeev wave function formalism, to which it reduces when n = 3. Except for the full breakup partition, which does not enter the equations, the new components are defined for all possible m-cluster partitions of the n-particles, 2 ≤ m ≤ n − 1. The sum of all the components yields the solution to the Schrödinger equation for scattering and either the Schrödinger equation solution or an easily identified spurious solution in the case of bound states. Both the two-cluster components and two-cluster transition operators are shown to be solutions of equations involving quantities carrying only two-cluster partition labels. Discussions of the Born term and a multiple scattering representation for the non-rearrangement transition operator and the inclusion of distortion operators in the formalism are also included.