Nuclear-atomic state degeneracy in neutrinoless double-electron capture: A unique test for a Majorana-neutrino

There is a general consensus that detection of a double-beta decay without any neutrino involved would mark physics beyond the Standard Model. This is because in such decay modes lepton number conservation would be violated and the neutrino would reveal itself as being its own antiparticle, thereby of Majorana type. So far, the experimental focus has mostly been on the double beta minus decay variant, where one attempts to measure the spectrum of the two emitted electrons. A discrete line at the endpoint energy marks the unique signature for a Majorana neutrino. Little attention has been given to alternative decay modes in double-beta decay. In this note we show that there is at least one case in the periodic table, where the parent in the neutrinoless double-electron capture process is nearly degenerate with an excited state in the daughter, leading to a possible enhancement of the decay rate by several orders of magnitude. It is the nucleus 74-Se, which has this unique property. Furthermore, there is an easy to detect 2 gamma-ray decay cascade in 74-Ge, which follows the zero-neutrino double electron capture, and which by its mere detection provides unique signature of the Majorana neutrino.