The possibility of observing the neutrinoless double $\beta$ decay and thus proving the Majorana nature of neutrinos as well as providing a sensitive measure of its mass is a major challenge of today’s neutrino physics. As an attractive alternative, we propose to study the inverse process—the radiative neutrinoless double-electron capture $\left(0\nu 2\mathrm{EC}\right)$. The associated monoenergetic photon provides a convenient experimental signature. Other advantages include the favorable ratio of the $0\nu 2\mathrm{EC}$ to the competing $2\nu 2\mathrm{EC}$ capture rates and, very importantly, the existence of a coincidence trigger to suppress the random background. These advantages partly offset the expected longer lifetimes. Rates for the $0\gamma 2\mathrm{EC}$ process are calculated. High $Z$ atoms are strongly favored. A resonance enhancement of the capture rates is expected to occur at an energy release comparable to the $2P\text{−}1S$ atomic level difference. The resonance conditions are likely to be met for decays to excited states in final nuclei. Candidates for such studies are considered. The experimental feasibility is estimated and found encouraging.

• Received 2 December 2003

DOI:https://doi.org/10.1103/PhysRevC.70.052501