Application of B3Y-Fetal Effective Interaction on Cluster Radioactivity

In this study, the B3Y-Fetal \(NN\) interaction, originating from the lowest order constrained variational approach (LOCV), is applied to investigate cluster radioactivity in energetically favoured trans-lead nuclei from \(^{221}\mathrm {Fr}\) to \(^{242}\mathrm {Cm}\) within the preformed cluster model, using the Wentzel–Kramers–Brillouin (WKB) theory. Five density-dependent parametrizations are considered to ascertain the most suitable one for cluster radioactivity. The statistical cluster preformation probability is employed and compared with the well-known empirical mass-dependent preformation factor. The predictive power of the BDB3Y1 and BDB3Y0 with the statistical probability is found to give the most accurate description of decay half-lives. These findings underscore the applicability of the B3Y-Fetal interaction in cluster radioactive decays and the reliability of statistical preformation probability in exploring similar decays within the uncharted region of the nuclear landscape. Furthermore, our results demonstrate that DDB3Y1 can aptly address the peculiarity and deviations known for \(^{14}\)C clusters, which is a strongly bound nucleus with \(N/Z = 1.33\). The extension of this study to the prediction of energetically favoured but unobserved cluster radioactive decays holds prospects for future experimental endeavours. Abstract Published by the Jagiellonian University 2026 authors