On neutrinoless double electron capture
  We found the probability for the neutrinoless double electron capture in the case of $KK$ capture. We clarified the mechanism of the energy transfer from the nucleus to the bound electrons. This enabled us to obtain the equations for the probability of the $2EC0\nu$ process which modify those obtained earlier. We found that the probability of the process is three orders of magnitude larger than it was supposed earlier. 
E. G. Drukarev, A. I. Mikhailov
nucl-th physics.atom-ph