Multiconfigurational-Dirac-Fock calculation of the 2s21S0–2s2p3P1spin-forbidden transition for the Be-like isoelectronic sequence

Accurate ab initio multiconfigurational-Dirac-Fock (MCDF) calculations of the lifetimes of the spin-forbidden 2${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$ ${\mathit{S}}_0$–2s2p ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_1$ transition and the allowed 2${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$ ${\mathit{S}}_0$–2s2p ${}_{}{}^1{}_{}{}^{}$ ${\mathit{P}}_1$ transition in Be-like ions have been performed. The importance of the inclusion of the Breit interaction to obtain accurate fine-structure splittings and mixing coefficients is discussed and the noted discrepancy between the length and velocity gauges for the intercombination line in the lighter ions is addressed. Different optimization procedures are evaluated. For C i i i the experimental intercombination transition rate has been measured to be 121.9 ${\mathrm{s}}^{\mathrm{-}1}$ with an accuracy of 6%. The current calculation gives 100.3±4 ${\mathrm{s}}^{\mathrm{-}1}$, in agreement with other recent calculations.