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.
U. D. Jentschura, "Two-Photon Decays Reexamined: Cascade Contributions and Gauge Invariance," Journal of Physics A: Mathematical and Theoretical, vol. 41, no. 15, IOP Publishing, Apr 2008.
The definitive version is available at https://doi.org/10.1088/1751-8113/41/15/155307
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01 Apr 2008