Calculation of nuclear matrix elements in neutrinoless double electron capture

We compute nuclear matrix elements for neutrinoless double electron capture on Gd-152, Er-164, and W-180 nuclei. Recent precise mass measurements for these nuclei have shown a large resonance enhancement factor that makes them the most promising candidates for observing this decay mode. We use an advanced energy density functional method which includes beyond mean-field effects such as symmetry restoration and shape mixing. Our calculations reproduce experimental charge radii and B(E2) values predicting a large deformation for all these nuclei. This fact reduces significantly the values of the NMEs leading to half-lives larger than 10(29) years for the three candidates.