Improved semi-empirical formula for cluster radioactivity half-lives

An improved semi-empirical formula for cluster radioactivity half-lives is proposed by incorporating the influences of reduced mass, the blocking effect of unpaired nucleons and mass asymmetry on the basis of the original Tavares formula Eur. Phys. J. A 49 (2013) 6. Using this improved semi-empirical formula, the calculated results of the cluster radioactivity half-lives for the daughter nuclei around Formula: see textPb or its neighbors can reproduce the experimental data well with a corresponding root-mean-square deviation Formula: see text= 0.570, which proves the feasibility of this formula to calculate cluster radioactivity half-lives in trans-lead nuclei. The accuracy of the improved semi-empirical formula is improved by approximately 37% compared to its predecessor whose the root-mean-square deviation is 0.902. Meanwhile, the influence of deformation effect for cluster radioactivity is also briefly discussed. In addition, we extend this improved semi-empirical formula to predict the half-lives of 51 possible cluster radioactive candidates whose cluster radioactivity are energetically allowed or observed but not yet quantified in NUBASE2020. For comparison, some empirical and/or semi-empirical formulae are also used.