Exploring cluster radioactivity and decay half-lives using different nuclear densities and approaches

The cluster decay half-lives and their decay characteristics are systematically investigated within the framework of the preformed cluster-decay model (PCM), focusing on the doubly closed-shell $^{208}\mathrm{Pb}$ daughter nucleus and extending the analysis to other daughter nuclei. The cluster-daughter interaction potential is calculated using the Skyrme energy density functional theory and a double-folding procedure with the M3Y nucleon-nucleon potential, incorporating densities derived from two different approaches: the phenomenological two-parameter Fermi (2pF) model and the microscopic Skyrme Hartree-Fock (SHF) radial densities. A key objective of the present work is to compare the 2pF and SHF densities to assess their impact on the cluster decay half-lives. The penetration probability through the interaction potential, a crucial factor in determining decay half-lives, is obtained using the Wentzel-Kramers-Brillouin approximation. The decay energies ($Q$ values) used in this work are calculated from various binding energy, including those from M"oller et al., Audi et al., the deformed relativistic Hartree--Bogoliubov theory in continuum (DRHBc), and the binding energy plus rotational correction energy from DRHBc calculations. These $Q$ values, in conjunction with the total interaction potential, serve as inputs in the PCM to compute the half-lives ${T}_{1/2}$ of experimentally observed clusters. It is observed that experimental $Q$ values reproduce the experimental half-lives well for all spherical cases considered, making them a more reliable choice for the spherical choice of the nuclei. By keeping the same $Q$ values, calculations for deformed nuclei are also carried out using experimental $Q$ values, incorporating deformation effects along with the optimal cold orientations. Furthermore, the standard deviation obtained for deformed nuclei is found to be nearly comparable to that of the spherical case, indicating the reliability of the PCM approach in both scenarios. Additionally, our analysis reveals that 2pF densities yield better agreement with experimental data compared to SHF densities, which may be attributed to their phenomenological nature, effectively capturing nuclear surface properties. The standard root-mean-square (rms) deviation for both the 2pF and SHF approaches could be further minimized if precise experimental half-lives were available for 15 of the 45 clusters considered in this study, for which only lower limits are currently available. The present analysis provides the theoretical predictions for the upcoming experiments on the heavier-mass region.