Systematic shell-model analysis of 2 ν1616 decay of 76 Ge and 96 Zr to the ground and excited states of 76 Se and 96 Mo

In this work, we have studied the 2 nu beta beta decay of 76 Ge and 96 Zr isotopes utilizing large-scale shell-model calculations. The GWBXG effective interaction has been employed in the calculation of 2 nu beta beta-decay nuclear matrix elements (NMEs). We have tested the effective interaction by comparing the predicted spectroscopic properties, such as energy spectra and transition probabilities, with the available experimental data. The variation of cumulative NMEs with respect to the 1+ state energies of the intermediate nucleus is also studied, corresponding to 0 + g . s . -> 0 + g . s . , 0 + g . s . -> 0+2 , and 0 + g . s . -> 2+1 transitions between the parent and grand-daughter nuclei. The effective values of axial-vector coupling strength ( g eff A ) are calculated using the predicted NMEs and experimental half-lives for 0 + g . s . shell-model predicted NMEs are consistent with the recent experimental data. The comparison of the shell-model predicted NMEs with previous NMEs available in the literature is discussed. Also, the computed branching ratios for the 2 nu beta beta decay of 76 Ge and both the 2 nu beta beta and single-beta decay of 96 Zr are reported corresponding to the calculated g eff A values. -> 0 + -> 0 + g.s. transitions. The extracted half-lives for 0 + 2 and 0 + g.s.g.s.-> 2+1 transitions using the