Perturbation Study of Some Excited States of Two-Electron Atoms

Abstract

A perturbation study of the $\mathrm{NP}$ states of two-electron atoms has been made. In particular, oscillator strength values for the ($1{}_{}{}^1{}_{}{}^{}S, 2{}_{}{}^1{}_{}{}^{}P$) and ($2{}_{}{}^3{}_{}{}^{}S, 2{}_{}{}^3{}_{}{}^{}P$) transitions are obtained. The $2{}_{}{}^1{}_{}{}^{}P$ and $2{}_{}{}^3{}_{}{}^{}P$ states are studied through ninth and tenth order, respectively. In addition, the $N{}_{}{}^1{}_{}{}^{}P$ and $N{}_{}{}^3{}_{}{}^{}P$ states are studied in first order through the $10P$ member of the series. Perturbation energy coefficients and other expectation values for several important operators have been computed. Perturbation energy coefficients for the $1{}_{}{}^1{}_{}{}^{}S$ state (through 25th order) and $2{}_{}{}^3{}_{}{}^{}S$ state (through 17th order) are also reported. Where comparison is possible, these results are in satisfactory agreement with the results obtained from variational calculations by C. L. Pekeris and co-workers. The variational-perturbation method for excited states requires auxiliary conditions on the perturbation wave functions. The condition on the $n\mathrm{th}$-order wave function is derived here. This is a generalization of the first-order condition given by Sinanoğlu.