On the atomic resonances in the $0\nu 2EC$ transitions

The nuclear method to discover Majorana neutrinos is the neutrinoless double $\beta$ decay. An interesting alternative is offered by the inverse process, neutrinoless radiative double electron capture, accompanied by a photon emission. Two different mechanisms seem plausible: the magnetic type radiation by an initial electron and the resonant electric type radiation by the final atom. The physical background for these processes is calculated.