An improved semi-empirical relationship for cluster radioactivity half-lives is proposed by introducing an accurate charge radius formula and an analytic expression of the preformation probability. Moreover, the cluster radioactivity half-lives for the daughter nuclei around ²⁰⁸Pb or its neighbors and the ¹²C radioactivity half-life of ¹¹⁴Ba are calculated within the improved semi-empirical relationship. It is shown that the accuracy of the new relationship is improved significantly compared to its predecessor. In addition, the cluster radioactivity half-lives that are experimentally unavailable for the trans-lead and trans-tin nuclei are predicted by the new semi-empirical formula. These predictions might be useful for searching for the new cluster emitters of the two islands in future experiments.

通过引入精确的电荷半径公式和预形成概率的解析表达式，提出了一种改进的团簇放射性半衰期半经验关系式。此外，子核的簇放射性半衰期约为²⁰⁸ Pb 或其邻居，¹² C 放射性半衰期为¹¹⁴Ba是在改进的半经验关系内计算的。结果表明，与之前的关系相比，新关系的准确性显着提高。此外，通过新的半经验公式预测了反式铅和反式锡核在实验上无法获得的簇放射性半衰期。这些预测可能有助于在未来的实验中寻找两个岛屿的新集群发射器。