Effect of shake-up on the rate of a neutrinoless double electronic capture in $^{164}$Er

TL;DR

This paper investigates how shake-off effects influence the rate of neutrinoless double electron capture in $^{164}$Er, revealing a significant increase in capture probability and implications for experimental detection.

Contribution

It introduces shake-off probability calculations that remove the resonance requirement, significantly increasing predicted capture rates and expanding candidate nuclei for experiments.

Findings

Capture rate increases by a factor of 5.6 due to shake-off.

Shake-off enhances electron capture from higher shells.

Potential to expand list of candidate nuclei for experiments.

Abstract

Traditionally double neutrinoless electronic capture is considered as a resonance process. We have fulfilled shake-off probability calculations, leading to ionization of the electron shell, in the case of $^{164}$Er. Allowance for the shake-off removes the requirement of resonance, leading to an increase of the capture rate. The contribution of the new mechanism increases the capture rate by a factor of 5.6 compared to the conventional resonance fluorescence mechanism. It also increases the probability of electron capture from higher shells, which must be foreseen in an experimental study. Moreover, effect of the shake-off can potentially expand the list of candidate nuclei for experiments.