Background: The cluster radioactivity from the neutron-deficient trans-tin region of the nuclear landscape has given immediate attention in the nuclear structure studies. Recent prediction of the emitting clusters from the ground and intrinsic excited states of proton-rich Ba isotopes opens the direction to explore the corresponding decay characteristics. A theoretical probe is necessary for understanding the cluster decays of Ba isotopes.

A new $\alpha$-emitting ²¹⁴U has been recently observed experimentally. This opens the window to theoretically investigate the ground-state properties of the lightest known even–even neutron deficient ^214,216,218U isotopes and to examine $\alpha$-particle clustering around the shell closure. The decay half-lives are calculated within the preformed cluster-decay model (PCM). To obtain the $\alpha$-daughter interaction potential, the RMF densities are folded with the newly developed R3Y and the well-known M3Y NN potentials for comparison. The alpha preformation probability $\left(P_{\alpha }\right)$ is calculated from the analytic formula of Deng and Zhang. The WKB approximation is employed for the calculation of the transmission probability. The individual binding energies (BE) for the participating nuclei are estimated from the relativistic mean-field (RMF) formalism and those from the finite range droplet model (FRDM) as well as WS3 mass tables. In addition to $Z=84$, the so-called abnormal enhancement region, i.e., $84\le Z\le 90$ and $N<126$, is normalised by an appropriately fitted neck-parameter $\Delta R$. On the other hand, the discrepancy sets in due to the shell effect at (and around) the proton magic number $Z=82$ and 84, and thus a higher scaling factor ranging from ${10}^{-8}$–${10}^{-5}$ is required. Additionally, in contrast with the experimental binding energy data, large deviations of about 5–10 MeV are evident in the RMF formalism despite the use of different parameter sets. An accurate prediction of $\alpha$-decay half-lives requires a Q-value that is in proximity with the experimental data. In addition, other microscopic frameworks besides RMF could be more reliable for the mass region under study. $\alpha$-particle clustering is largely influenced by the shell effect.

Background: The theoretical and experimental investigations of decay properties of heavy and superheavy nuclei are crucial to explore the nuclear structure and reaction dynamics. Purpose: The aim of this study is to probe the α-decay properties of ²⁴³Fm and ²⁴⁵Fm isotopic chains using relativistic mean-field (RMF) approach within the framework of preformed cluster-decay model (PCM). Methods: The RMF densities are folded with the relativistic R3Y NN potential to deduce the nuclear interaction potential between the α particle and daughter nucleus. The penetration probability is calculated within the WKB approximation. Results: The α-decay half-lives of even-odd ²⁴³Fm and ²⁴⁵Fm isotopes and their daughter nuclei are obtained from the preformed cluster-decay model. These theoretically calculated half-lives are found to be in good agreement with the recent experimental measurements. Conclusions: The novel result here is the applicability of the scaling factor within the PCM as a signature for shell/sub-shell closures in α-decay studies. As such, we have also demonstrated that N=137, 139 and Z=94 corresponding to ^231,233Pu could be shell/sub-shell closures. The least T_1/2 is found at ^243,245Fm which indicate their individual stability and α-decay as their most probable decay mode.

There is no analytical solution to the Schrödinger equation for the many-electron systems. Whereas a numerical solution, which perfectly possible in theory, is impossible in practice for systems containing multiple nuclei and electrons due to the finite speed and memory of computers. The Skyrme interaction is an effective density-dependent nucleon-nucleon force which has been widely employed in the past decades by the nuclear-physics community within the non-relativistic Hartree-Fock framework. Hartree-Fock calculations with this interaction have been performed over a wide range of the periodic table, providing results compatible to the experimental values for total binding energies, nuclear radii, deformations and single-particle level ordering. Here we briefly review the recent progress on the Skyrme Hartree-Fock Model and current applications in nuclear physics.

This study explores the cluster decay half-lives in both experimentally measured and undetected radioactive nuclei within the mass number range The investigation employs the recently proposed preformation probability formula, focusing on the systematic behaviours governing cluster emissions. Emphasis is placed on the contribution of the Q-value during both preformation and decay processes. Experimental binding energy data are used to estimate Q-values, and the cluster penetration process is discussed using the M3Y and R3Y nuclear potentials. The interaction potential between the cluster and the daughter nucleus is obtained by folding the relativistic mean-field (RMF) densities with R3Y NN potential using the NL3* parameter set and compared with the phenomenological M3Y NN potential. The penetration probabilities are calculated from the WKB approximation. The formula is found to be a useful tool for understanding cluster radioactivity in heavy actinides. The result provides valuable insights into the systematics of cluster decay half-lives, highlighting the influence of neutron magic shell closures and interaction potentials on different cluster decay properties.