Calculation of nuclear matrix elements in neutrinoless double electron capture

TL;DR

This paper calculates nuclear matrix elements for neutrinoless double electron capture in specific nuclei using advanced methods, predicting very long half-lives and highlighting the importance of nuclear deformation effects.

Contribution

It introduces a sophisticated energy density functional approach including beyond mean-field effects to compute NMEs for these decay modes, improving accuracy.

Findings

Large deformation reduces NME values significantly.

Predicted half-lives exceed 10^29 years for all candidates.

Resonance enhancement makes these nuclei promising for detection.

Abstract

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.