Cluster radioactivity preformation probability of trans-lead nuclei in the NpNn scheme

In the present work, the cluster radioactivity preformation probability Pc in the scheme of NpNn for the effective number of the valence particles (holes) in trans-lead nuclei has been systematically investigated. This quantity has been explored in the simplified parametrization of NpNn as well as the multiplication NpNnI of this product with the isospin asymmetry I. The calculations for Pc are both performed in microscopic and model-dependent way. Within the microscopic approach, based on our previous work [Chin. Phys. C 47, 014101 (2023)], Pc is calculated in cluster formation model combined with the exponential relationship of Pc to the & alpha; decay preformation probability P & alpha; when the mass number of the emitted cluster Ac 28. While Ac 28, Pc is obtained through the charge-number dependence of Pc on the decay products proposed by Ren et al. [Phys. Rev. C 70, 034304 (2004)]. In the model-dependent approach, Pc is extracted through the ratios from calculated cluster radioactivity half-lives in the framework of unified fission model proposed by Dong et al. [Eur. Phys. J. A 41, 197 (2009)] to experimental ones. Both of the results show Pc in logarithmic form are linear to NpNn as well as NpNnI. For comparison, the parent-mass-number dependence analytical formula as well as the model proposed by Wei and Zhang [Phys. Rev. C 96, 021601(R) (2017)] are also used. Furthermore, the preformation mechanic for cluster radioactivity has also been discussed.

Automated summary

In this study, the preformation probability Pc of cluster radioactivity in the NpNn scheme for the effective number of valence particles in trans-lead nuclei was investigated. Pc was explored in a microscopic and model-dependent way. The results showed that Pc is linearly related to NpNn and NpNnI, and different approaches were used to calculate Pc.