  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.
