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Two-photon decay rates in simple atoms such as hydrogenlike systems representrather interesting fundamental problems in atomic physics. The sum of theenergies of the two emitted photons has to fulfill an energy conservationcondition, the decay takes place via intermediate virtual states, and the totaldecay rate is obtained after an integration over the energy of one of theemitted photons. Here, we investigate cases with a virtual state having anenergy intermediate between the initial and the final state of the decayprocess, and we show that due to non-uniform convergence, only a carefultreatment of the singularities infinitesimally displaced from the photonintegration contour leads to consistent and convergent results.

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