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 ( ), we systematically investigate the cluster radioactivity half-lives of 22 trans-lead nuclei ranging from 221 Fr to 242 Cm. When the mass number of the emitted cluster 28, is obtained by the exponential relationship of to the α decay preformation probability ( ) proposed by R. Blendowskeis [Phys. Rev. Lett. 61 , 1930 (1988)], while is calculated through the cluster-formation model (CFM). When 28, is calculated through the charge-number dependence of on the decay products proposed by Ren [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 [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.