Systematic study of cluster radioactivity within the generalized liquid drop model*

Abstract

The cluster radioactivity is studied within the Generalized Liquid Drop Model (GLDM), in which the shell correction energy, the pairing energy, and the cluster preformation factor are considered. The calculations show significant improvements and can reproduce the experimental data within a factor of 8.04 after the consideration of these physical effects. In addition, the systematic trend of cluster preformation factors $P_c$ is discussed in terms of the $N_pN_n$ scheme to study the influence of valence proton-neutron interaction and shell effect on cluster radioactivity. It is strikingly found that the $\log_{10}{P_c}$ is linearly related to the $N_pN_n$. It is in agreement with the recent work [L. Qi \textit{et al.}, \href{https://journals.aps.org/prc/abstract/10.1103/PhysRevC.108.014325}{Phys. Rev. C 108, 014325 (2023)}], in which $\log_{10}{P_c}$, obtained by using different theoretical models and treatment methods from this work, also has a linear relationship with $N_pN_n$. Combined with recent work by Qi \textit{et al.}, this work suggests that the linear relationship between $\log_{10}{P_c}$ and $N_pN_n$ is model-independent and that both the shell effect and the valence proton-neutron interaction play essential roles in cluster radioactivity. An analytical formula is proposed to calculate the cluster preformation factor based on the $N_pN_n$ scheme. In addition, the cluster preformation factors and cluster radioactivity half-lives of some heavy nuclei are predicted, which can provide references for experiments in the future.