Systematic calculations of cluster radioactivity half-lives in trans-lead nuclei* *This work is supported in part by the National Natura Science Foundation of China (12175100 and 11975132), the Construct Program of the Key Discipline in Hunan Province, the Research Foundation of Education Bureau of Hunan Province (18A237), the Natural Science Foundation of Hunan Province (2018JJ3324), the Innovation Group of Nuclear and Particle Physics in USC, the Shandong Province Natural Science Foundation (ZR2015AQ007), the National Innovation Training Foundation of China (201910555161), and the Opening Project of Cooperative Innovation Center for Nuclear Fuel Cycle Technology and Equipment, University of South China (2019KFZ10).

Abstract

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 221Fr to 242Cm. 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.