Our study consists of investigations of nuclear ground state properties and weak transition rates of even-even waiting point nuclei. The calculation was performed for $N=50$ and $N=82$ nuclei. The Relativistic Mean Field (RMF) model was used to explore the nuclear ground state properties of selected nuclei. The proton-neutron quasi particle random phase (pn-QRPA) model was used for the computation of allowed Gamow Teller (GT) and unique first-forbidden (U1F) transitions of the selected waiting point nuclei. The RMF approach with different density-dependent interactions, DD-ME2 and DD-PC1, was used to compute potential energy curves and surfaces, quadrupole moments, deformation parameters, binding energies, proton-neutron separation energies, charge, and radii. The RMF computed deformation parameters were used in the pn-QRPA model, as a free parameter, for the computation of GT and U1F weak transitions. We investigated three different sets of deformation parameter for the calculation of electron emission rates. The rates changed considerably with change in deformation parameter. We later investigated contribution of allowed GT and U1F rates and competition between positron capture and electron emission rates at high stellar temperatures. The computed positron capture rates were significant especially at low densities and high temperatures. The contribution of U1F rates to allowed GT appreciably reduced the total calculated half-lives. The comparison of our results with previous calculations and measurement is also shown. The pn-QRPA calculation including U1F contribution is in good agreement with the experimental data.

我们的研究包括对偶偶等待点核的核基态特性和弱跃迁率的研究。计算是为了$N=50$ 和 $N=82$核。相对论平均场 (RMF) 模型用于探索选定原子核的核基态特性。质子-中子准粒子随机相位 (pn-QRPA) 模型用于计算所选等待点核的允许 Gamow Teller (GT) 和唯一的第一禁止 (U1F) 跃迁。具有不同密度依赖相互作用的 RMF 方法，DD-ME2 和 DD-PC1，用于计算势能曲线和表面、四极矩、变形参数、结合能、质子-中子分离能、电荷和半径。RMF 计算的变形参数在 pn-QRPA 模型中用作自由参数，用于计算 GT 和 U1F 弱过渡。我们研究了用于计算电子发射率的三组不同的变形参数。速率随着变形参数的变化而显着变化。我们后来研究了在高恒星温度下允许的 GT 和 U1F 速率的贡献以及正电子捕获和电子发射速率之间的竞争。计算出的正电子捕获率非常显着，尤其是在低密度和高温下。U1F 率对允许 GT 的贡献明显减少了总计算半衰期。还显示了我们的结果与以前的计算和测量的比较。包括 U1F 贡献的 pn-QRPA 计算与实验数据非常吻合。计算出的正电子捕获率非常显着，尤其是在低密度和高温下。U1F 率对允许 GT 的贡献明显减少了总计算半衰期。还显示了我们的结果与以前的计算和测量的比较。包括 U1F 贡献的 pn-QRPA 计算与实验数据非常吻合。计算出的正电子捕获率非常显着，尤其是在低密度和高温下。U1F 率对允许 GT 的贡献明显减少了总计算半衰期。还显示了我们的结果与以前的计算和测量的比较。包括 U1F 贡献的 pn-QRPA 计算与实验数据非常吻合。