Spontaneous two-photon decay rates in hydrogenlike and heliumlike ions

A theoretical study of the two-photon emission rate from the 1s2s ¹S state of two-electron ions is presented. High-precision values of the nonrelativistic emission rate for ions with nuclear charge Z up to 36 are obtained by use of correlated variational wave functions of the Hylleraas type. Summations over intermediate states are performed by finite-basis-set methods. The results are used to obtain an accurate extrapolation formula and to study the convergence characteristics of a 1/Z expansion for the decay rate. The leading hydrogenic term is calculated to an accuracy which substantially exceeds Klarsfeld's, and the next term is obtained for what is believed to be the first time. Relativistic effects are taken into account by means of a screened hydrogenic approximation. The predicted decay rate for two-electron Kr³⁴⁺ is (2.993±{}0.012)×{}10¹⁰ s^-1, where the error is the uncertainty in the relativistic correction. This lies significantly higher than the value (2.934±{}0.030)×{}10¹⁰ s^-1 recently measured by Marrus et al.