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 $^{2}P^{o}$ and $^{2}S^{e}$ levels in the Li isoelectronic sequence, $Z=1 \mathrm{to} 10$, are presented. The results of calculations for the energies of $^{2}D^{e}$ triply excited states in ${\mathrm{He}}^{\ensuremath{-}}$ are also reported. The calculated energies are compared with available experimental and other theoretical values. Finally, the lowest $^{2}S^{e}$ and two lowest $^{2}P^{o}$ energy levels in the isoelectronic sequence are fitted by a $\frac{1}{Z}$ perturbation expansion. It is seen that this expansion can be used to estimate the energy levels of such states for higher nuclear charges.