  Two-photon decay rates in simple atoms such as hydrogenlike systems represent
rather interesting fundamental problems in atomic physics. The sum of the
energies of the two emitted photons has to fulfill 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
energy intermediate between the initial and the final state 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.
