Systematic calculations of cluster radioactivity half-lives with a screened electrostatic barrier

TL;DR

This study presents a systematic model based on WKB theory that incorporates screened electrostatic effects to accurately calculate cluster radioactivity half-lives across a range of nuclei, and extends predictions to unmeasured candidates.

Contribution

The paper introduces a phenomenological model with two adjustable parameters that effectively reproduces experimental data and predicts half-lives of potential cluster emitters, considering electrostatic screening effects.

Findings

Model achieves rms deviation of 0.660 with experimental data.

Predicted half-lives are consistent with other theoretical models.

Extended predictions include unmeasured cluster radioactivity candidates.

Abstract

In the present work, based on Wentzel-Kramers-Brillouin theory, we systematically study the cluster radioactivity half-lives of 22 nuclei ranging from $^{221}$$\rm{Fr}$ to $^{242}$$\rm{Cm}$ by using a phenomenological model, which considers the screened electrostatic effect of Coulomb potential. In this model, there are two adjustable parameters i.e. the parameter $t$ and $g$, which are related to the screened electrostatic barrier and the strength of spectroscopic factor, respectively. The calculated results indicate this model can well reproduce the experimental data while the corresponding root-mean-square (rms) deviation is 0.660. In addition, we extend this model to predict the half-lives of possible cluster radioactive candidates whose cluster radioactivity are energetically allowed or observed but not yet quantified in the evaluated nuclear properties table NUBASE2020. The predicted results are consistent with the ones obtained by using other theoretical models and/or empirical formulae including the universal decay law (UDL) proposed by Qi \textit{et al.} [Phys. Rev. C 80, 044326 (2009)], a semi-empirical model for both $\alpha$ decay and cluster radioactivity proposed by Santhosh \textit{et al.} [J. Phys. G 35, 085102 (2008)] and a unified formula of half-lives for $\alpha$ decay and cluster radioactivity proposed by Ni \textit{et al.} [Phys. Rev. C 78, 044310 (2008)].