Cluster decay half-lives of trans-lead nuclei within the Coulomb and proximity potential model

Within the Coulomb and proximity potential model (CPPM) the cluster decay process in 199–226Fr, 206–232Ac, 209–237Th, 212–238Pa, 217–241U, 225–242Np, 225–244Pu, 231–246Am, 202–230Ra and 233–249Cm isotopes leading to the doubly magic 208Pb and neighboring nuclei are studied. The computed half-lives are compared with available experimental data and are in good agreement with each other. The half-lives are also computed using the Universal formula for cluster decay (UNIV) of Poenaru et al., Universal Decay Law (UDL) and the Scaling Law of Horoi et al., and their comparisons with CPPM values are found to be in agreement. The calculations for the emission of 22O from the parent 209–237Th, 20O from the parents 202–230Ra and 217–240U, were the experimental values are not available are also done. It is found that most of the decay modes are favorable for measurement image, and this observation will serve as a guide to the future experiments. The odd–even staggering (OES) are found to be more prominent in the emission of odd mass clusters. The Geiger–Nuttall plots of image versus image for various clusters ranging from image to image from different isotopes of heavy parent nuclei with atomic numbers within the range image have been studied and are found to be linear. Our study reveals the role of doubly magic image daughter nuclei in cluster decay process and also reveal the fact that the role of neutron shell closure is crucial than proton shell closure.