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

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 $101.6\pm 0.7\hspace{0.5em}{\sec }^{-1}$ differs from the measured value of $102.94\pm 0.14\hspace{0.5em}{\sec }^{-1}$ [Doerfert et al., Phys. Rev. Lett. 78, 4355 (1997)] by about 1.3%.