Two-Photon Decays Reexamined: Cascade Contributions and Gauge Invariance

TL;DR

This paper recalculates two-photon decay rates in hydrogenlike ions, clarifies the treatment of photon emission processes, and explicitly demonstrates gauge invariance within a nonrelativistic framework.

Contribution

It provides new numerical calculations of two-photon decay rates and clarifies the gauge invariance and cascade contributions in these processes.

Findings

Decay rates scale as (Z alpha)^6/n^3

Gauge invariance of decay rates is explicitly shown

Clarification of cascade versus simultaneous photon emission

Abstract

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 hydrogenlike 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 (Z alpha)^6/n^3, where alpha 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.