Double electron capture by proton-rich nuclei is a second-order nuclear process analogous to double beta decay. Despite their similarities, the decay signature is quite different, potentially providing a new channel to measure the hypothesized neutrinoless mode of these decays. The Standard-Model-allowed two-neutrino double electron capture ($2 u ECEC$) has been predicted for a number of isotopes, but only observed in $^{78}$Kr, $^{130}$Ba and, recently, $^{124}$Xe. The sensitivity to this decay establishes a benchmark for the ultimate experimental goal, namely the potential to discover also the lepton-number-violating neutrinoless version of this process, $0 u ECEC$. Here we report on the current sensitivity of the NEXT-White detector to $^{124}$Xe $2 u ECEC$ and on the extrapolation to NEXT-100. Using simulated data for the $2 u ECEC$ signal and real data from NEXT-White operated with $^{124}$Xe-depleted gas as background, we define an optimal event selection that maximizes the NEXT-White sensitivity. We estimate that, for NEXT-100 operated with xenon gas isotopically enriched with 1 kg of $^{124}$Xe and for a 5-year run, a sensitivity to the $2 u ECEC$ half-life of $6 times 10^{22}$ y (at 90% confidence level) or better can be reached.
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