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Double-weak decays of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Xe</mml:mi><mml:mprescripts/><mml:none/><mml:mn>124</mml:mn></mml:mmultiscripts></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Xe</mml:mi><mml:mprescripts/><mml:none/><mml:mn>136</mml:mn></mml:mmultiscripts></mml:math> in the XENON1T and XENONnT experiments
We present results on the search for double-electron capture ($2\nu\text{ECEC}$) of $^{124}$Xe and neutrinoless double-$\beta$ decay ($0\nu\beta\beta$) of $^{136}$Xe in XENON1T. We consider captures from the K- up to the N-shell in the $2\nu\text{ECEC}$ signal model and measure a total half-life of $T_{1/2}^{2\nu\text{ECEC}}=(1.1\pm0.2_\text{stat}\pm0.1_\text{sys})\times 10^{22}\;\text{yr}$ with a $0.87\;\text{kg}\times\text{yr}$ isotope exposure. The …