Non-Uniform Convergence of Two-Photon Decay Rates for Excited Atomic States

Author

Ulrich D. Jentschura, Missouri University of Science and TechnologyFollow

Abstract

Two-photon decay rates in simple atoms such as hydrogen-like systems represent rather interesting fundamental problems in atomic physics. The sum of the energies of the two emitted photons has to fulfil an energy conservation condition, the decay takes place via intermediate virtual states, and the total decay rate is obtained after an integration over the energy of one of the emitted photons. Here, we investigate cases with a virtual state having an intermediate energy between the initial and the final states of the decay process, and we show that due to non-uniform convergence, only a careful treatment of the singularities infinitesimally displaced from the photon integration contour leads to consistent and convergent results.

Recommended Citation

U. D. Jentschura, "Non-Uniform Convergence of Two-Photon Decay Rates for Excited Atomic States," Journal of Physics A: Mathematical and Theoretical, vol. 40, no. 9, pp. F223 - F227, IOP Publishing, Mar 2007.

The definitive version is available at https://doi.org/10.1088/1751-8113/40/9/F02

Department(s)

Physics

International Standard Serial Number (ISSN)

1751-8113

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2007 IOP Publishing, All rights reserved.

Publication Date

01 Mar 2007