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

In this work, we have studied the 2νββ decay of ⁷⁶Ge and ⁹⁶Zr isotopes utilizing large-scale shell-model calculations. The GWBXG effective interaction has been employed in the calculation of 2νββ-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 granddaughter nuclei. The extracted half-lives using the shell-model predicted NMEs show good agreement 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 2νββ decay of ⁷⁶Ge and both the 2νββ and single-β decay of ⁹⁶Zr are reported.