Measurements and models of enhanced recombination following inner-shell vacancies in liquid xenon

Electron-capture decays of $^{125}$Xe and $^{127}$Xe, and double-electron-capture decays of $^{124}$Xe, are backgrounds in searches for weakly interacting massive particles (WIMPs) conducted by dual-phase xenon time projection chambers such as LUX-ZEPLIN (LZ). These decays produce signals with more light and less charge than equivalent-energy $\beta$ decays, and correspondingly overlap more with WIMP signals. We measure three electron-capture charge yields in LZ: the 1.1~keV M-shell, 5.2~keV L-shell, and 33.2~keV K-shell at drift fields of 193 and 96.5~V/cm. The LL double-electron-capture decay of $^{124}$Xe exhibits even more pronounced shifts in charge and light. We provide a first model of double-electron-capture charge yields using the link between ionization density and electron-ion recombination, and identify a need for more accurate calculations. Finally, we discuss the implications of the reduced charge yield of these decays and other interactions creating inner-shell vacancies for future dark matter searches.