Large-scale relativistic configuration-interaction calculation of the 2s^{2} ^{1}S_{0}–2s2p ^{3}P_{1} intercombination transition in C III

Abstract

A large-scale, relativistic configuration-interaction (RCI) method has been developed for precision calculations of transition oscillator strengths. It is based on the no-pair Hamiltonian and employs finite B-spline basis functions. For the ${2s}^{2}{}^{1}{S}_{0}--2s2p{}^{3}{P}_{1}$ intercombination transition in berylliumlike carbon, the present RCI expansions reach close to 200 000 configurations, and include all single and double excitations from valence-valence, core-valence, and core-core interactions, along with dominant triple and quadruple excitations. Resulting length- and velocity-gauge transition rates are very well converged, but still differ by a factor of 2. This strong gauge dependence is found to arise from the neglect of negative-energy states which has negligible effects on length-gauge results but can affect velocity-gauge results significantly. The present intercombination transition rate for C III of $101.6\ifmmode\pm\else\textpm\fi{}0.7 {\mathrm{sec}}^{\ensuremath{-}1}$ differs from the measured value of $102.94\ifmmode\pm\else\textpm\fi{}0.14 {\mathrm{sec}}^{\ensuremath{-}1}$ [Doerfert et al., Phys. Rev. Lett. 78, 4355 (1997)] by about 1.3%.