Triply excited states of three-electron atomic systems

A formalism is discussed whereby many-electron systems may be described by a great number of product functions of different configurations in a manageable way. Calculations are made to find triply excited energy levels of three-electron atomic systems, using products of hydrogenic functions with a Z equal to that of the nucleus. Results for the lowest ²Pᵒ and ²Sᵉ levels in the Li isoelectronic sequence, Z=1 to 10, are presented. The results of calculations for the energies of ²Dᵉ triply excited states in He^- are also reported. The calculated energies are compared with available experimental and other theoretical values. Finally, the lowest ²Sᵉ and two lowest ²Pᵒ energy levels in the isoelectronic sequence are fitted by a 1/Z perturbation expansion. It is seen that this expansion can be used to estimate the energy levels of such states for higher nuclear charges.