IMPORTANCE OF PREFORMATION PROBABILITY IN CLUSTER RADIOACTIVE-DECAYS USING RELATIVISTIC MEAN FIELD THEORY WITHIN THE PREFORMED CLUSTER MODEL

Using the preformed cluster model (PCM) of Gupta and collaborators, we have deduced empirically the preformation probability P0emp from experimental data on both the α and exotic-cluster radioactive decays in the trans-lead region having doubly magic 208 Pb or its neighboring nuclei as daughters, using the spherical and (in some cases) deformed relativistic mean field (RMF) densities. For spherical considerations, the P0α(emp) for alpha-decays is almost constant ~ 10-2 - 10-3 for all the parent nuclei studied, and P0c(emp) for cluster-decays of the same parents decrease with increasing size of cluster. The results obtained for spherical P0c(emp) are within two to three orders of magnitude of the well accepted phenomenological formula of Blendowske-Walliser (BW), which led us to propose a new empirical formula. The use of deformed RMF densities, however, tend to bring the results closer to BW formula.