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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 $T^{2\nu{\rm
ECEC}}_{1/2}=(1.3-18)\times 10^{22}$ y for the ET and $T^{2\nu{\rm ECEC}}_{1/2}
= (0.43-2.9)\times 10^{22}$ 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.