Abstract
We investigate the possibilities of observing the decay mode for $^{124}$Xe in which two electrons are captured, two neutrinos are emitted, and the final daughter nucleus is in its ground state, using dark matter experiments with liquid xenon. The first upper limit of the decay half-life is calculated to be 1.66$\times10^{21}$ years at a 90% confidence level (C.L.) obtained with the published background data from the XENON100 experiment. Employing a known background model from the Large Underground Xenon (LUX) experiment, we predict that the detection of double-electron capture of $^{124}$Xe to the ground state of $^{124}$Te with LUX will have approximately 115 events, assuming a half-life of 2.9 $\times$ 10$^{21}$ years. We conclude that measuring $^{124}$Xe 2$\nu$ double-electron capture to the ground state of $^{124}$Te can be performed more precisely with the proposed LUX-Zeplin (LZ) experiment.
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