Shell model predictions for $^{124}$Sn double-beta decay

TL;DR

This paper uses shell model calculations to predict the two-neutrino double-beta decay half-life of $^{124}$Sn and provides nuclear matrix elements for neutrinoless decay mechanisms, aiding future experimental efforts.

Contribution

The study offers novel shell model predictions for $^{124}$Sn double-beta decay half-lives, contrasting with previous QRPA results, and supplies nuclear matrix elements for neutrinoless decay mechanisms.

Findings

Shell model predicts $2 u eta eta$ decay half-life significantly different from QRPA.

Provides nuclear matrix elements for $0 u eta eta$ decay mechanisms.

Results will guide future experimental searches.

Abstract

Neutrinoless double-beta ($0 \nu \beta \beta$) decay is a promising beyond Standard Model process. Two-neutrino double-beta ($2 \nu \beta \beta$) decay is an associated process that is allowed by the Standard Model, and it was observed in about 10 isotopes, including decays to the excited states of the daughter. $^{124}$Sn was the first isotope whose double-beta decay modes were investigated experimentally, and despite few other recent efforts, no signal has been seen so far. Shell model calculations were able to make reliable predictions for $2 \nu \beta \beta$ decay half-lives. Here we use shell model calculations to predict the $2 \nu \beta \beta$ decay half-life of $^{124}$Sn. Our results are quite different from the existing quasiparticle random-phase approximation (QRPA) results, and we envision that they will be useful for guiding future experiments. We also present shell model nuclear matrix elements for two potentially competing mechanisms to the $0 \nu \beta \beta$ decay of $^{124}$Sn.