Two-photon decay rates in heliumlike ions: Finite-nuclear-mass effects

Abstract

The spontaneous two-photon decay rates from the $1s2s\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$ level to the ground state $1{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$ in helium and its isoelectronic ions through neon ($Z=10$) are calculated, including the effects of finite nuclear mass. In all cases the length and velocity results agree to eight or more figures, demonstrating that the theoretical formulation correctly takes into account the effects of mass scaling, mass polarization, and motion of the nucleus in the center-of-mass frame. Algebraic relationships are derived and tested relating the expansion coefficients in powers of $\ensuremath{\mu}/M$ for mass polarization, where $\ensuremath{\mu}$ is the electron reduced mass and $M$ is the nuclear mass. Muonic, pionic, and antiprotonic helium are included as extreme test cases where mass polarization is large. The results are compared with experiment and previous calculations.