Hyperspherical hierarchy of three-electron radial excitations

Abstract

We investigate hierarchical representation of three-electron radial excitations, relying on the replacement of a sequence of ordered individual electron radial coordinates by a hierarchical sequence of hyperspherical radial variables. In the spirit of the hyperspherical method we argue that the latter variables allow adiabatic quasiseparability of the three-electron wave function. We examine this by approximately evaluating hyperspherical adiabatic potential curves and channel functions for the Li${(s}^{3})$ configuration. The hierarchical representation permits one to display manifold aspects of the triply excited states with a pair of radial quantum numbers.