  The possibility to observe the neutrino-less double $ \beta $ decay and thus
to prove the Majorana nature of neutrino as well as provide a sensitive measure
of its mass is a major challenge of to-day's neutrino physics. As an attractive
alternative we propose to study the inverse process, the radiative
neutrino-less double electron capture $0 \nu 2EC$. The associated monoenergetic
photon provides a convenient experimental signature. Other advantages include
the favourable ratio of the $0 \nu 2EC$ to the competing $2\nu 2EC$ capture
rates and, very importantly, the existence of coincidence trigger to suppress
the random background. These advantages partly offset the expected longer
lifetimes. Rates for the $0\gamma 2EC$ process are calculated. High Z atoms are
strongly favoured. A resonance enhancement of the capture rates is predicted at
energy release comparable to the $2P-1S$ 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 highly encouraging.
