Shake-off in the Er164 neutrinoless double-electron capture and the dark matter puzzle

Traditionally neutrinoless double-electronic capture is considered as a resonance process. Degeneracy of the initial and daughter nuclei is the main factor mastering the decay rate. We have fulfilled shake-off probability calculations. Allowance for the shake-off loosens the need for resonance, leading to a radical increase of the capture rate in the nonresonance nuclei. In the case of $^{164}\mathrm{Er}$, the contribution of the new mechanism increases the capture rate by a factor of 5.6. It also increases the probability of electron capture from higher shells. The influence of the shake-off is also expected to manifest itself in the other $\ensuremath{\beta}$ processes which are used in the studies of the neutrino nature, its mass and role in the dark matter puzzle.