Variational Bethe-Goldstone calculations of atomic oscillator strengths. Be sequence

Atomic oscillator strengths have been computed by applying a Bethe-Goldstone hierarchy of variational calculations consistently to both initial and final states of a given transition. For the $1s^2{}_{}{}^1{}_{}{}^{}S\to 1s2p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ transitions in the He isoelectronic sequence, computed $f_l$ (length) and $f_v$ (velocity) values and the corresponding transition energies are in good agreement with the accurate $f$ values of Pekeris et al. and with observed transition energies. For the Be isoelectronic sequence, $f_l$ and $f_v$ for $1s^{2}2s^2{}_{}{}^1{}_{}{}^{}S\to 1s^{2}2s2p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ are in close agreement with each other if all double virtual excitations from $1s2s2p$ (with respect to $1s^{2}2s2p$ as reference configuration) are included in the variational calculations. The agreement between computed and observed transition energies is very good. Similar results have been obtained for other valence shell excitations of Be i: $2s2p{}_{}{}^3{}_{}{}^{}P_{}^o{}_{}{}^{}\to 2p^2{}_{}{}^3{}_{}{}^{}P$, $2s2p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}\to 2p^2{}_{}{}^1{}_{}{}^{}D$, $2s2p{}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}\to 2p^2{}_{}{}^1{}_{}{}^{}S$. The $2p^2{}_{}{}^1{}_{}{}^{}S$ state apparently lies slightly above the Be ii $2s$ threshold. The $2p^2{}_{}{}^1{}_{}{}^{}D$ state interacts strongly with the $2s3d{}_{}{}^1{}_{}{}^{}D$ Rydberg state. The oscillator strength is nearly zero for the ${}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}\to {}_{}{}^1{}_{}{}^{}D$ transition.