Systematic study of cluster radioactivity within the generalized liquid drop model* *Supported by the National Natural Science Foundation of China (12175170), Hubei Provincial Natural Science Foundation of China (2023AFB035), Hunan Outstanding Youth Science Foundation (2022JJ10031), and Natural Science Research Project of Yichang City (A23-2-028)

Abstract

Cluster radioactivity is studied within the generalized liquid drop model (GLDM), in which the shell correction energy, pairing energy, and cluster preformation factor are considered. The calculations show significant improvements and can reproduce the experimental data within a factor of 8.04 after considering these physical effects. In addition, the systematic trend of the cluster preformation factors is discussed in terms of the scheme to study the influence of the valence proton-neutron interaction and shell effect on cluster radioactivity. It is found that is linearly related to . This is in agreement with a recent study [L. Qi et al., Phys. Rev. C 108, 014325 (2023)], in which , obtained using different theoretical models and treatment methods than those used in this study, also had a linear relationship with . Combined with the work by Qi et al., this study suggests that the linear relationship between and is model-independent and both the shell effect and valence proton-neutron interaction play essential roles in cluster radioactivity. An analytical formula is proposed to calculate the cluster preformation factor based on the scheme. In addition, the cluster preformation factors and the cluster radioactivity half-lives of some heavy nuclei are predicted, which can provide a reference for future experiments.