Two-photon electron capture by H-like uranium

We present a study of two -photon electron capture by H -like uranium ions. The energy of the incident electron was chosen to be in the region with the most significant contribution of the dielectronic recombination. We studied the photon emission spectrum. In particular, we calculated the differential over the photon energy cross section including the main resonance groups corresponding to the cascade transitions, and the low -energy photon region, where the infrared divergence required special processing. The calculations were performed within the framework of QED theory. The importance of generalized Breit interaction was discussed. We investigated the roles of the dielectronic recombination and the radiative recombination. We investigated the resonance approximation and the single -photon approximation, which are commonly used to describe radiation spectra.