Double-βtransformations in isobaric triplets with mass numbersA=124, 130, and 136

The Q values of double-electron capture in ${}^{124}$Xe, ${}^{130}$Ba, and ${}^{136}$Ce and double-beta decay of ${}^{124}$Sn and ${}^{130}$Te have been determined with the Penning-trap mass spectrometer SHIPTRAP with a few hundred eV uncertainty. These nuclides are members of three isobaric triplets with common daughter nuclides. The main goal of this work was to investigate the existence of the resonant enhancement of the neutrinoless double-electron-capture rates in ${}^{124}$Xe and ${}^{130}$Ba in order to assess their suitability for the search for neutrinoless double-electron capture. Based on our results, in neither of these cases is the resonance condition fulfilled.