We compute nuclear matrix elements for neutrinoless double electron capture on $^{ 152}$Gd, $^{ 164}$Er and $^{ 180}$W 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.
Categories: nucl-th nucl-ex