Two-neutrino double electron capture on ${}^{124}$Xe based on an effective theory and the nuclear shell model

Abstract

We study the two-neutrino double electron capture on ${}^{124}$Xe based on an effective theory (ET) and large-scale shell model calculations, two modern nuclear structure approaches that have been tested against Gamow-Teller and double-beta decay data. In the ET, the low-energy constants are fit to electron capture and ${\beta }^{-}$ transitions around xenon. For the nuclear shell model, we use an interaction in a large configuration space that reproduces the spectroscopy of nuclei in this mass region. For the dominant transition to the ${}^{124}$Te ground state, we find half-lives $T_{1/2}^{2\nu \mathrm{ECEC}}=(1.3-18)\times 10^{22}$ y for the ET and $T_{1/2}^{2\nu \mathrm{ECEC}}=(0.43-2.9)\times 10^{22}$ y for the shell model. The ET uncertainty leads to a half-life almost entirely consistent with present experimental limits and largely within the reach of ongoing experiments. The shell model half-life range overlaps with the ET, but extends less beyond current limits. Our findings thus suggest that the two-neutrino double electron capture on ${}^{124}$Xe has a good chance to be discovered by ongoing or future experiments. In addition, we present results for the two-neutrino double electron capture to excited states of ${}^{124}$Te.

5 pages, 2 figures

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