Systematic calculations of cluster radioactivity half-lives in trans-lead nuclei

TL;DR

This study systematically calculates cluster radioactivity half-lives in trans-lead nuclei using WKB theory, considering various preformation probabilities and models, and compares results with existing models to improve predictive accuracy.

Contribution

It introduces a comprehensive approach combining different preformation probability models and extends predictions to unmeasured nuclei, enhancing the understanding of cluster radioactivity.

Findings

Calculated half-lives agree well with experimental data.

The proposed models outperform previous semi-empirical models.

Extended predictions for 51 nuclei with unknown or unquantified cluster radioactivity.

Abstract

In the present work, based on Wentzel-Kramers-Brillouin (WKB) theory, considering the cluster preformation probability (Pc), we systematically investigate the cluster radioactivity half-lives of 22 trans-lead nuclei ranging from 221Fr to 242Cm. As for Pc, when the mass number of the emitted cluster Ac<28, it is obtained by the exponential relationship of Pc to the alpha decay preformation probability Pa proposed by R.Blendowskeis et al. [Phys. Rev. Lett. 61, 1930 (1988)], while Pa is calculated through cluster-formation model (CFM). Whereas Ac >= 28, it is achieved through the charge-number dependence of Pc on the decay products proposed by Ren et al. [Phys. Rev. C 70, 034304 (2004)]. The half-lives of cluster radioactivity have been calculated by the density-dependent cluster model [Phys. Rev. C 70, 034304 (2004)] and by the unified formula of half-lives for alpha decay and cluster radioactivity [Phys. Rev. C 78, 044310 (2008)]. For comparison, a universal decay law (UDL) proposed by Qi et al. [Phys. Rev. C 80, 044326 (2009)], a semi-empirical model for both alpha decay and cluster radioactivity proposed by Santhosh [J. Phys. G: Nucl. Part. Phys. 35, 085102 (2008)] and a unified formula of half-lives for alpha decay and cluster radioactivity [Phys. Rev. C 78, 044310 (2008)] are also used. The calculated results in our work, Ni's formula as well as UDL can well reproduce the experimental data and are better than those in Santhosh's model. In addition, we extend this model to predict the half-lives for 51 nuclei, whose cluster radioactivity is energetically allowed or observed but yet not quantified in NUBASE2020.