Two-Photon Decays Reexamined: Cascade Contributions and Gauge Invariance

The purpose of this paper is to calculate the two-photon decay rate corresponding to the two-photon transitions nS → 1S and nD → 1S in hydrogen-like ions with a low nuclear charge number Z (for principal quantum numbers n = 2, ..., 8). Numerical results are obtained within a nonrelativistic framework, and the results are found to scale approximately as (Zα) 6/n3, where α is the fine-structure constant. We also attempt to clarify a number of subtle issues regarding the treatment of the coherent, quasi-simultaneous emission of the two photons as opposed to one-photon cascades. In particular, the gauge invariance of the decay rate is shown explicitly