Adiabatic energies and perturbative non-adiabatic corrections for Coulombic three-particle systems in the hyperspherical harmonics formalism

Abstract

The adiabatic energies and non-adiabatic corrections of the bound and lowest-lying quasi-bound S states of the light Coulombic three-particle systems, the negative positronium and muonium ions and the neutral He atom, are evaluated using the hyperspherical harmonics formalism. The calculations are based on the adiabatic separation of the hyperradial and the hyperangular degrees of freedom. The non-adiabatic corrections are determined using high-order Rayleigh-Schrödinger perturbation theory. Although the adiabatic perturbation series do not always converge, they can be accurately summed for isolated states applying Wynn's algorithm. The perturbation treatment exhibits high numerical stability with respect to the number of basis functions and it is therefore possible to perform these calculations employing very large basis set expansions. The perturbation series pertaining to the well-isolated ground states are summable even in the diabatic representation.