1Zexpansion study of the(1s)22sS2and(1s)22pP2states of the lithium isoelectronic sequence

A $\frac{1}{Z}$ expansion method is used to calculate the eigenvalues and eigenfunctions for the ${\mathrm{}\left(1s\right)\mathrm{}}^{2}2s{}_{}{}^2{}_{}{}^{}S$ and ${\mathrm{}\left(1s\right)\mathrm{}}^{2}2p{}_{}{}^2{}_{}{}^{}P$ states of the lithium isoelectronic sequence. The dipole-length and dipole-velocity forms of the oscillator strengths for the $2s-2p$ resonance transitions are compared with the results of direct variational calculations for individual values of the nuclear charge $Z$. It is explicitly demonstrated that the length formulation of the dipole matrix element is more accurate than the velocity formulation for the $2s-2p$ transitions.