On the resonant neutrinoless double-electron-capture decay of Ce

The double-electron-capture Q value for the ¹³⁶Ce decay to ¹³⁶Ba has been determined at JYFLTRAP. The measured value 2378.53(27) keV excludes the energy degeneracy with the ⁰⁺$0^{+}$ excited state of the decay daughter ¹³⁶Ba at 2315.32(7) keV in a resonant 0νECEC$0\nu \mathrm{ECEC}$ decay by 11.67 keV. The new Q value differs from the old adopted value 2419(13) keV (Atomic Mass Evaluation 2003) by 40 keV and is 50 times more precise. Our calculations show that the precise Q   value renders the resonant 0νECEC$0\nu \mathrm{ECEC}$ decay of ¹³⁶Ce undetectable by the future underground detectors. We measured also the double-β decay Q value of ¹³⁶Xe to be 2457.86(48) keV which agrees well with the value 2457.83(37) keV measured at the Florida State University.