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

In the present work, based on the 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 from221Fr to242Cm. When the mass number of the emitted cluster Ac< 28, Pcis obtained by the exponential relationship of Pcto the α decay preformation probability(P α) proposed by R. Blendowskeis et al. [Phys. Rev.Lett. 61, 1930(1988)], while P α is calculated through the cluster-formation model(CFM). When Ac≥ 28, Pcis calculated through the charge-number dependence of Pcon the decay products proposed by Ren et al. [Phys. Rev. C70, 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 α 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 of our work, Ni’s formula, and the UDL can well reproduce the experimental data and are better than those of 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 not yet quantified in NUBASE2020.