Approximate analytical solution of the quantum-mechanical three-body Coulomb continuum problem

Abstract

In this work a symmetric representation of the three-body Coulomb continuum wave function is constructed that represents an exact asymptotic solution of the many-body Schrödinger equation on a five-dimensional hypersphere of large hyperradius. Consequently, the wave function is shown to satisfy the Kato cusp conditions at all three two-body collision points. At finite distances the proposed solution is designed to account for properties of the total potential surface. In particular, dynamical stabilization due to the presence of ridge structure in the total potential (Wannier ridge) is encompassed in the present treatment. The behavior of the wave function at the total dissociation threshold is investigated. In order to allow for three-body interactions we linearly expand each two-body Coulomb potential in terms of all three two-body potentials. The expansion coefficients determine the amount of distortion of each two-body subsystem by the presence of the third particle and thus give direct information on the strength of three-body interactions. © 1996 The American Physical Society.