Dirac-Hartree-Fock calculation of the 2 S 1 3 → 1 S 0 1 transition rates for the He isoelectronic sequence

A new calculation of the $M1$ decay rates of the metastable $2^{3}S_{1}$ states of two-electron ions is presented. The calculation is based on the Furry bound-interaction representation of quantum electrodynamics and expansion in powers of $\ensuremath{\alpha}Z$ is avoided. The basic one-electron states are constructed from solutions to the Dirac equation including the ground-state Dirac-Hartree-Fock potential. Correlation and transverse-photon-exchange effects, both of relative order ${Z}^{\ensuremath{-}1}$, are included in the calculation by the perturbation expansion of the $S$ matrix in powers of $\ensuremath{\alpha}$. Decay rates calculated to lowest order in powers of $\ensuremath{\alpha}$ are smaller than previously reported rates. When correlation and transverse-photon-exchange corrections are included in the calculation the resulting rates agree well with previous calculations. We estimate that the present values are more accurate than the older results for $Zg12$, while for smaller $Z$ the older results are expected to be better. The close agreement between the present calculations and previous theoretical results confirms the smallness of both higher-order relativistic effects and of higher-order correlation corrections in calculations of this type.