Theoretical analysis and predictions for the two-neutrino double electron capture of ¹²⁴Xe

Abstract We provide a complete theoretical description of the two-neutrino electron capture in 124 Xe, improving both the nuclear and the atomic structure calculations. We improve the general formalism through the use of the Taylor expansion method, leading to higher-order terms in the decay rate of the process. The nuclear part is treated with pn-QRPA and interacting shell model (ISM) methods. The nuclear matrix elements (NMEs) are calculated with the pn-QRPA method with isospin restoration by fixing the input parameters so that the experimental decay rate is reproduced, resulting in values significantly lower than in previous calculations. The validity of the pn-QRPA NMEs is tested by showing their values to be comparable with the ones for double-beta decay with the emission of two antineutrinos of 128,130 Te, which have similar pairing features. Within the ISM, we reproduce the total experimental half-life within a factor of two and predict the capture fraction to the KK channel of about 74%. We also predict the capture fractions to other decay channels and show that for the cumulative decay to the KL 1 –KO 1 channels, a capture fraction of about 24% could be observed experimentally. On the atomic side, calculations are improved by accounting for the Pauli blocking of the decay of innermost nucleon states and by considering all s -wave electrons available for capture, expanding beyond the K and L 1 orbitals considered in previous studies. We also provide improved atomic relaxation energies of the final atomic states of 124 Te, which may be used as input for background modeling in liquid Xenon experiments.