Matrix elements of the two-neutrino double beta decay of 76Ge using deformed BCS and Lipkin-Nogami approaches

Herein, the effect of quadrupole deformation has been thoroughly studied using the generalized BCS and Lipkin-Nogami (LN) pairing approaches for both like- and unlike-particle pairing modes. The pairing treatment of the realistic NN-interaction with these two approaches is then used to calculate the two-neutrino double beta decay matrix elements, (MGT2ν), through the Quasiparticle Random Phase Approximation (QRPA) theory. The results reveal significant differences in the calculated matrix elements due to the inclusion of the unlike-particle pairing mode, besides a small difference in MGT2ν values regarding the pairing approach type used in calculations. It is found that, the competition between the BCS and LN approaches in the calculation of MGT2ν, slightly depends on the inclusion or exclusion of the pn-pairing mode.