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. ${}^{124}\mathrm{Sn}$ 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 ${}^{124}\mathrm{Sn}$. Our results are quite different from the existing quasiparticle random-phase approximation 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 ${}^{124}\mathrm{Sn}$.

• Received 28 August 2015
• Revised 11 November 2015

DOI:https://doi.org/10.1103/PhysRevC.93.024308