Exploring the Systematics of Cluster Decay Half-Lives in Heavy Actinides Within the Range 234 < A < 252

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.