An improved semi-analytic approach to the barrier penetration probability is developed in the frame work of the Wentzel-Kramers-Brillouin (WKB) approximation. It is used to calculate decay half-lives and preformation probabilities for a set of 304 cluster emitters in the range 87 ≤ Z ≤ 96 and a set of 390 α-emitters in the range 52 ≤ Z ≤ 120. For cluster decay, the validity of our approach is tested against Coulomb and proximity potential model (CPPM) by comparing decay half-lives and barrier penetration probabilities. Our results are found to be in a good agreement with CPPM calculations and with the available experimental data. In case of α-decay, our calculations are tested against the experimental data and also a very good agreement is achieved. In both cases, results are also compared with calculations of some other well known universal decay laws that are used in many recent studies. Our approach shows a better agreement with experimental data than most of the other models. Our study is extended to calculate the assault frequency and preformation probability of the cluster inside the parent nucleus. A strong correlation is obtained for all these parameters with each other. Neutron shell closures are found to be more important in the cluster decay process than proton shell closure. It is also noted that the odd-even staggering behavior dominates the decay processes involving the emission of clusters with odd neutron number.

中文翻译：

---

簇衰变半衰期和预形成概率

在 Wentzel-Kramers-Brillouin (WKB) 近似的框架中开发了一种改进的屏障穿透概率的半解析方法。它用于计算 87 ≤ Z ≤ 96 范围内的一组 304 个簇发射器和 52 ≤ Z ≤ 120 范围内的一组 390 个α-发射器的衰减半衰期和预形成概率。 对于簇衰减，有效性通过比较衰变半衰期和势垒穿透概率，我们的方法针对库仑和邻近电位模型 (CPPM) 进行了测试。发现我们的结果与 CPPM 计算和可用的实验数据非常吻合。在α衰变的情况下，我们的计算根据实验数据进行了测试，并且也达到了非常好的一致性。在这两种情况下，结果还与许多最近研究中使用的其他一些众所周知的普遍衰变定律的计算进行了比较。与大多数其他模型相比，我们的方法与实验数据显示出更好的一致性。我们的研究扩展到计算母核内星团的攻击频率和预形成概率。所有这些参数之间都获得了很强的相关性。发现中子壳闭合在簇衰变过程中比质子壳闭合更重要。还注意到奇偶交错行为主导了涉及奇数中子数团簇发射的衰变过程。我们的研究扩展到计算母核内星团的攻击频率和预形成概率。所有这些参数之间都获得了很强的相关性。发现中子壳闭合在簇衰变过程中比质子壳闭合更重要。还注意到奇偶交错行为主导了涉及奇数中子数团簇发射的衰变过程。我们的研究扩展到计算母核内星团的攻击频率和预形成概率。所有这些参数之间都获得了很强的相关性。发现中子壳闭合在簇衰变过程中比质子壳闭合更重要。还注意到奇偶交错行为主导了涉及奇数中子数团簇发射的衰变过程。