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Two-photon decays reexamined: cascade contributions and gauge invariance

Ulrich D Jentschura 2008 J. Phys. A: Math. Theor. 41 155307 (13pp)   doi: 10.1088/1751-8113/41/15/155307  Help

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Ulrich D Jentschura
Max-Planck-Institut für Kernphysik, Postfach 10 39 80, 69029 Heidelberg, Germany
and
Institut für Theoretische Physik, Philosophenweg 16, 69120 Heidelberg, Germany

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 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.

PACS numbers: 31.30.J−, 12.20.Ds, 32.80.Wr, 31.15.−p

Print publication: Issue 15 (18 April 2008)
Received 31 December 2007, in final form 18 February 2008
Published 2 April 2008

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