Dynamics of competing α and cluster radioactive decays within the collective clusterization approach

The purpose of this work is to study the dynamics of competing α and 208Pb daughter cluster radioactive decays using the preformed cluster decay model (PCM), within the collective clusterization approach of Quantum Mechanical Fragmentation Theory (QMFT). The QMFT based fragmentation potential comprises of binding energy (B.E) (which is the sum of liquid drop energy (VLDM), based on semi empirical mass formula of Seeger and shell corrections (δU) given by Myers and Swiatecki), Coulomb potential (VC) and nuclear proximity potential (VP) of the cluster and daughter nuclei in the ground state decay of the radioactive parent nuclei. To explore the competing aspects of α and 208Pb daughter cluster radioactivities, we have chosen 222Ra, 226Th, 228Th, 231Pa, 230U and 232U parent nuclei. The crucial role played by shell closure effects is demonstrated in minimized values of fragmentation potential for cluster accompanied by doubly-magic 208Pb daughter nucleus in comparison to neighboring fragments. The higher values of preformation probabilities, P0 of these clusters further reveal significance of nuclear structure in the cluster radioactivity process. We have calculated the half-lives via fragmentation potential, preformation probability, scattering potential for spherical case, of chosen nuclei, and then compared with the given experimental data. From the comparison of α cluster and 208Pb daughter decays, we see that the former is heavily dominating with larger values of P0 in comparison to the later as evident from the experimentally observed high count rate of α cluster in such decays. However, the penetrability for both types of decays is almost similar. The experimental data and PCM calculated results are in fair comparison for all the chosen cases.