Cluster decay half-lives in heavy nuclei: comparative study of DFM and CPPM and the development of the Santhosh’s formula

The importance of this research lies in enhancing the theoretical understanding of the cluster decay phenomenon as a rare occurrence that provides vital information about nuclear stability. Its importance is further manifested through the ability of the studied models to predict the properties of magic nuclei and those close to them, thereby supporting research in both theoretical and practical fields. However, there is a research gap due to the limitations of traditional semi-empirical formulas, such as the Santhosh formula, which depend on general statistical data without considering the fine details of nuclear structure or charge density distribution. Additionally, there is a need to test the efficiency of models that integrate nuclear potential and inter-nuclear distances, such as Double-Folding Model (DFM) and Coulomb and Proximity Potential Model (CPPM), in accurately predicting half-life and to compare their results more thoroughly with experimental values. This research aims to compare the DFM, CPPM, and Santhosh formula to evaluate their accuracy in calculating the logarithm of half-life, while also developing the Santhosh formula parameters using software adaptation. This study shows the effect of both and on the stability of the nuclei, and the nature of the relationship between these two variables, based on an analytical approach depending on the structure and density of the nucleus. The charge in DFM and the potential near the nucleus surface in CPPM, a programming approach using the Python language to develop the Santhosh parameters, and a comparative approach using standard deviation were used. The results showed a clear improvement in the performance of the Santhosh model by 13% after adjusting the parameters, which contributed to reducing the standard deviation of 1.87, with the DFM model having the lowest standard deviation of 0.47, followed by the CPPM model with a value of 0.59. It also showed that the and the are the two main factors determining the half-life, and that the probability of cluster formation decreases with a clear increase in its mass number. Therefore, it can be concluded that the DFM and CPPM models are promising and have provided excellent accuracy with experimental data.