Precise calculation of nuclear matrix element for the 2νECEC decay of ¹²⁴Xe

The first observation of the half-life for the 2vECEC decay of ¹²⁴Xe was recently reported by the XENON collaboration (Nature 568, 532(2019), Phys. Rev. C 106, 024328 (2022)). Previous theoretical calculations of the nuclear matrix element and half-life describing the transition (Phys. Lett. B 797, 134885 (2019), J. Phys. G 40, 075102 (2013)) show large discrepancies when compared with the experimental result. We provide a new shell model calculation of the nuclear matrix element in the jj55model space (g7/2 sd, h11/2 orbitals) and, when used with updated space phase factors, it provides a 2vECEC half-life of ¹²⁴Xe that is within a factor of two of the experimental result. This calculation reinforces our previous prediction of the 2vββ decay of ¹²⁴Sn (Phys. Rev. C 93, 024308 (2016)).