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. It is this particle-antiparticle duality which makes the neutrino of Majorana type. So far, the experimental focus has been on the β−β− decay variant only, where one attempts to measure the spectrum of the two emitted electrons. A discrete line at the endpoint energy is 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 (0νεε decay) is nearly degenerate with an excited state in the daughter, leading to an enhancement of the decay rate by several orders of magnitude. It is the nucleus Se, which has this unique property. Furthermore, there is an easy to detect 2γ ray decay cascade in Ge, which follows the 0νεε, and which by its mere detection provides unique signature of the Majorana neutrino.