### 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.

Original language | English |
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Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 40 |

Issue number | 9 |

DOIs | |

Publication status | Published - Mar 2 2007 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Modelling and Simulation
- Statistics and Probability

### Cite this

**Non-uniform convergence of two-photon decay rates for excited atomic states.** / Jentschura, U.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Non-uniform convergence of two-photon decay rates for excited atomic states

AU - Jentschura, U.

PY - 2007/3/2

Y1 - 2007/3/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=42649108514&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=42649108514&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/40/9/F02

DO - 10.1088/1751-8113/40/9/F02

M3 - Article

AN - SCOPUS:42649108514

VL - 40

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 9

ER -