Nuclear matrix elements and half-lives for two neutrino <i>β</i> ⁺ <i>β</i> ⁺, <i>ϵβ</i> ⁺ and <i>ϵϵ</i> decays of ¹²⁴Xe

Abstract Nuclear matrix elements for 2 νβ + β + , 2 νϵβ + and 2 νϵϵ transitions to the ground state and the first 2 + state of 124 Te have been calculated by considering the restoration of SU(4) symmetry violations within the framework of proton-neutron quasi-particle random phase approximation (pn-QRPA) method. The decays to the final excited states have a negligible effect on the total decay probability due to their very small phase-space factors. A comparison of the calculated values with the shell model results clearly shows the quenching effect of the restoration on the decay rates. Thus, the calculated half-life for double electron capture ( ϵϵ ) transition to the final ground state is one order of magnitude higher than the corresponding experimental data.