Theory of Relativistic Magnetic Dipole Transitions: Lifetime of the Metastable2S3State of the Heliumlike Ions

It has recently been established that the radiative lifetime of the metastable $2{}_{}{}^3{}_{}{}^{}S$ state of helium and the heliumlike ions is determined by single-photon magnetic dipole ($M1\mathrm{}$) transitions to the ground state, rather than the two-photon process proposed by Breit and Teller. The theory of $nl-n^{\prime }l$ $M1\mathrm{}$ transitions with $n\ne n^{\prime }$ is developed in the Pauli approximation and extended to two-electron systems. Terms arising from relativistic energy corrections and finite-wavelength effects are included. The results for hydrogenic systems are shown to be identical to those obtained in the relativistic four-component Dirac formulation. The coefficients in the $Z^{-1\mathrm{}}$ perturbation expansion of the $1s2s{}_{}{}^3{}_{}{}^{}S-1s^2{}_{}{}^1{}_{}{}^{}S$ $M1\mathrm{}$ transition integral are evaluated through ninth order and used to calculate the $M1\mathrm{}$ emission probabilities from the $2{}_{}{}^3{}_{}{}^{}S$ state of the two-electron ions up to Fe XXV. The emission probability for neutral helium is 1.27 × ${10}^{-4\mathrm{}}$ ${\sec }^{-1\mathrm{}}$. The results are compared with recent solar coronal observations by Gabriel and Jordan, and with a measurement of the $2{}_{}{}^3{}_{}{}^{}S$ state lifetime in Ar XVII by Schmieder and Marrus.