S,P, andDstates of three-electron ions viaZ-dependent perturbation theory

A perturbation study of the $1s^2\mathrm{ns}{}_{}{}^2{}_{}{}^{}S,1\mathrm{}{s}^2\mathrm{np}{}_{}{}^2{}_{}{}^{}P$, and $1s^2\mathrm{nd}{}_{}{}^2{}_{}{}^{}D$ states of three-electron atoms has been made (for $n=3\mathrm{} \mathrm{to} 7$). Second- order energy coefficients for these states are calculated, and estimates of the relativistic corrections to low orders in $Z$ are also obtained. Transition energies computed with these results, however, are not of high accuracy when compared to the experimental data, particularly for low-$Z$ members of the isoelectronic sequence. Introduction of higher-order energy coefficients can correct this deficiency, but these coefficients are difficult to compute. A semiempirical fitting of the experimental data is used here to obtain estimates of these higher-order coefficients with little computational effort. These, in turn, yield transition energies in excellent agreement with experiment.