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

The adiabatic energies and non-adiabatic corrections of the bound and lowes t-lying quasi-bound S states of the light Coulombic three-particle systems, the negative positronium Ps(-) and muonium Mu(-) ions and the neutral He(1 s(2)) 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 dete rmined using high-order Rayleigh-Schrodinger perturbation theory. Although the adiabatic perturbation series do not always converge, they can be accur ately summed for isolated states applying Wynn's epsilon algorithm. The per turbation treatment exhibits high numerical stability with respect to the n umber of basis functions and it is therefore possible to perform these calc ulations employing very large basis set expansions. The perturbation series pertaining to the well-isolated ground states are summable even in the dia batic representation.