2S13→1S01+onephotontransition in heliumlike ions: Exact result for the lowest-order effect of the electron-electron interaction

Abstract

The decay rate $R$ for the $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\to 1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}+\mathrm{one}\mathrm{photon}$ transition in heliumlike ions is studied for large $Z$. We write $R=R^{\mathrm{}\left(0\right)\mathrm{}}(1+\frac{b_1}{Z}+\cdots )$ and evaluate $b_1$ exactly with the help of Schwinger's integral representation of the Coulomb Green's function. The result supports the accuracy of the variational wave functions obtained by Drake. In view of the results of recent theoretical work on radiative and recoil corrections, we conclude that the rates predicted by pure quantum electrodynamics are known to considerable precision. The discrepancy between the theory and experiment for several values of $Z$ is briefly discussed.