Relativistic calculation of the 21S0–21,3P1transitions in berylliumlike molybdenum and berylliumlike iron

The $2^{1,3}$ ${\mathit{P}}_{1–}$2 ${}_{}{}^1{}_{}{}^{}$ ${\mathit{S}}_0$ transitions in berylliumlike molybdenum and berylliumlike iron have been calculated including all-order relativistic correlations due to the Coulomb as well as the Breit interaction. Important correlation corrections to the radiative contributions to the ground state were found due to the large admixture of ${\mathit{p}}^2$ character in the 2 ${}_{}{}^1{}_{}{}^{}$ ${\mathit{S}}_0$ wave function. Comparison with experiment is done after the addition of the Lamb shift for the corresponding hydrogenlike systems and an estimate of the screening caused by the 1${\mathit{s}}^2$ electrons. The results of ${\mathrm{Mo}}^{38+}$ are 725 751±300 and 2 004 464±300 ${\mathrm{cm}}^{\mathrm{-}1}$ for the 2 ${}_{}{}^1{}_{}{}^{}$ ${\mathit{S}}_{0–}$2 ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_1$ and 2 ${}_{}{}^1{}_{}{}^{}$ ${\mathit{S}}_{0–}$2 ${}_{}{}^1{}_{}{}^{}$ ${\mathit{P}}_1$ transitions, respectively, which agree well with the experimental results 725 758±158 and 2 003 847±1200 ${\mathrm{cm}}^{\mathrm{-}1}$. The corresponding results for ${\mathrm{Fe}}^{22+}$ are 379 118±90 and 752 459±90 ${\mathrm{cm}}^{\mathrm{-}1}$, which can be compared to the experimental values 379 140±20 and 752 372±57 ${\mathrm{cm}}^{\mathrm{-}1}$. The uncertainty in the theoretical value is completely dominated by the uncertainty in the evaluation of the radiative effects in the electronic field.