Triply excited states of three-electron atomic systems

Abstract

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, $Z=1\mathrm{} \mathrm{to} 10$, are presented. The results of calculations for the energies of ${}_{}{}^2{}_{}{}^{}D_{}^e{}_{}{}^{}$ triply excited states in ${\mathrm{He}}^{-}$ 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.