Large-scale shell-model calculations have been performed for the study of two-neutrino double-beta ($2\nu \beta \beta$) decay in ⁸²Se, ⁹⁴Zr, ¹⁰⁸Cd, ¹²⁴Sn, ¹²⁸Te, ¹³⁰Te, ¹³⁶Xe, and ¹⁵⁰Nd. We have employed JUN45 interaction to calculate the nuclear matrix element (NME) for $2\nu \beta \beta$ decay in ⁸²Se. In the case of ⁹⁴Zr, the glekpn effective interaction is used. For ¹⁰⁸Cd, we have used a realistic effective interaction derived through the G-matrix approach. In the case of ¹²⁴Sn, ^128,130Te and ¹³⁶Xe, the sn100pn effective interaction is employed. For ¹⁵⁰Nd, we have used KHHE effective interaction based on holes in a ²⁰⁸Pb core. We have extracted the half-lives of these nuclei for the $2\nu \beta \beta$ decay with the help of calculated NME. Our results are consistent with the available experimental half-lives. The variation of cumulative $2\nu \beta \beta$ NME with respect to the excitation energy of the intermediate $1^{+}$ states is also shown, and in all cases, it is ensured that their values are almost saturated. In the present work we have calculated more intermediate $1^{+}$ states as much as possible in comparison to results available in the literature.

已经对两个中微子双β（$2\nu \beta \beta$) ⁸² Se、⁹⁴ Zr、¹⁰⁸ Cd、¹²⁴ Sn、¹²⁸ Te、¹³⁰ Te、¹³⁶ Xe 和¹⁵⁰ Nd 中的衰变。我们采用 JUN45 相互作用来计算核基质元素 (NME)$2\nu \beta \beta$⁸² Se中的衰变。对于⁹⁴ Zr，使用 glekpn 有效相互作用。对于¹⁰⁸ Cd，我们使用了通过 G 矩阵方法导出的真实有效交互作用。^在124 Sn、^128,130 Te 和¹³⁶ Xe的情况下，采用 sn100pn 有效相互作用。对于¹⁵⁰ Nd，我们使用了基于²⁰⁸ Pb 核心中的空穴的 KHHE 有效相互作用。我们提取了这些原子核的半衰期$2\nu \beta \beta$在计算的 NME 的帮助下进行衰减。我们的结果与现有的实验半衰期一致。累积变化$2\nu \beta \beta$NME 相对于中间体的激发能$1^{+}$状态也被显示，并且在所有情况下，确保它们的值几乎饱和。在目前的工作中，我们计算了更多的中间值$1^{+}$尽可能多地说明与文献中可用结果的比较。