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 α decay preformation probability (Pα) proposed by R.Blendowskeis et al. [Phys. Rev. Lett. 61, 1930 (1988)], while Pα 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 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 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.

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In the present work, derived from Balasubramaniam’s formula [Phys. Rev. C 70, 017301 (2004)], further&#xD;considering the effects of parent nucleus mass, blocking effect and reduced mass on cluster radioactivity half-lives, we propose a new Geiger-Nuttall law which is model-independent for systematically evaluating the half-lives of this process for 10 even-even nuclei&#xD;and 16 odd-A nuclei. For comparison, a single universal curve for cluster radioactivities and α decay proposed by&#xD;D. N. Poenaru [Phys. Rev. C 83, 014601 (2011)], a scaling law proposed by M. Horoi [J. Phys. G: Nucl. Part.&#xD;Phys. 30, 945 (2004)], an extension of Viola-Seaborg formula from α decay to cluster radioactivity proposed by Ren&#xD;et al. [Phys. Rev. C 70, 034304 (2004)], a new semi-empirical formula for exotic cluster decay proposed by M.&#xD;Balasubramaniam et al. [Phys. Rev. C 70, 017301 (2004)] and a unified formula of half-lives for α decay and cluster&#xD;radioactivity proposed by Ni et al. [Phys. Rev. C 78, 044310 (2008)] are also used. The calculated results of our&#xD;new Geiger-Nuttall law are in good agreement with the experimental half-lives with the least rms being 0.605 and are&#xD;better than the compared ones. Moreover, we extend this formula to predict the cluster radioactivity half-lives&#xD;of 51 nuclei whose decay energy are energetically allowed or observed but not yet quantified in NUBASE2020.

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