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 P(0)(emp) from experimental data on both the a 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 P(0)(alpha(emp)) for alpha-decays is almost constant similar to 10(-2) - 10(-3) for all the parent nuclei studied, and P(0)(c(emp)) for cluster-decays of the same parents decrease with increasing size of cluster. The results obtained for spherical P(0)(c(emp)) are within two to three orders of magnitude of the well accepted phenomenological formula of Blendowske-Walliser (DW), 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.