铅外区团簇放射性：修正经验公式的系统研究
Cluster radioactivity in trans-lead region: A systematic study with modified empirical formulas
摘要：
本文采用几个经验公式，通过加入角动量（$l$）或同位旋相关（$I=(N-Z)/A$）或两者同时加入，对周期表中trans-lead（86 $\leq$ Z $\leq$ 96）区域的团簇衰变半衰期进行了修正，较全面地探讨了团簇发射的可能性。这些修改后的版本的公式被发现具有较小的$χ^2$每自由度和均方根误差，除了一些其他的统计参数的较小的值，而与它们相应的旧版本相比，在现有的61个实验数据的集群放射性。通过应用Balasubramaniam \textit{et al.} [PRC 70（2004）017301]给出的公式的修改版本，其中最精确的公式，系统地预测了几个簇的半衰期，即Be、B、C、N、O、F、Ne、Na、Mg和Si的同位素在反式铅区域中的几个同位素。以分支比的形式研究了团簇发射与$α$衰变的竞争，它把几种可能的团簇发射带入了这些核的可能衰变模中。这种集群的半衰期的准确预测，预计将是至关重要的未来的实验观测，其中$α$ -衰变观察占主导地位。
英文摘要：
The possibility of cluster emission from trans-lead (86$\leq$Z$\leq$96) region of periodic chart has been explored comprehensively by employing few empirical formulas which are modified by adding angular momentum ($l$) or isospin-dependent ($I=(N-Z)/A$) or both terms for the calculation of cluster decay half-lives. These modified versions of the formulas are found with lesser $χ^2$ per degree of freedom and root mean-square error, in addition to the smaller values of some other statistical parameters, while compared to their corresponding old versions on available 61 experimental data of cluster radioactivity. By applying the modified version of the formula given by Balasubramaniam \textit{et al.} [PRC 70 (2004) 017301], the most accurate formula among these, half-lives of several clusters i.e. isotopes of Be, B, C, N, O, F, Ne, Na, Mg, and Si are predicted systematically for the several isotopes in the trans-lead region. The contest of cluster emission with $α$-decay has been investigated in form of branching ratio which brings several potential cluster emissions into the probable decay modes of these nuclei. The accurate prediction of half-lives of such clusters is expected to be crucial for the future experimental observations where $α$-decay is observed dominantly.
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