jeudi 3 juin 2010 à 12:20
Cluster radioactivity (CR) is the spontaneous emission of clusters heavier than α-particle. Since its first theoretical prediction in 1980 and experimental confirmation in 1984, this phenomenon is now established for some 26 decays with light to heavy (14C to 34Si) clusters from various actinides (221Fr to 242Cm). Theoretically, two types of models have been advanced, namely, (i) the Unified fission models (UFM), such as the analytic super-asymmetric fission model (ASAFM), and (ii) the Preformed cluster models (PCM) based on quantum mechanical fragmentation theory (QMFT). The UFM and PCM differ from each other for their not-inclusion or inclusion of pre-formation or spectroscopic factors of the clusters being formed (or born) before penetrating the confining interaction barriers. Due to the very importance of preformation/spectroscopic factor from the point of view of including nuclear structure information, in this study, based on PCM, we use for the first time the relativistic mean field (RMF) theory, which is already shown to support the clustering effects in various heavy parents with observed cluster decays. Following the PCM approach, we have deduced empirically the preformation probability P0emp from the experimental data for both the α- and exotic cluster-decays, specifically of parents in the trans-lead region having doubly magic 208Pb or its neighboring nuclei as daughters. We have explored here mainly the significance of the pre-formation factor in the two processes. The calculations involve four independent steps: First, the cluster and daughter matter densities are calculated as the RMF densities. Using the double folding procedure, these densities are then folded with M3Y plus zero-range pseudo-potential (the exchange effects, EX), to obtain the nuclear interaction potential. As a next step, the WKB penetration probability P is calculated by using the experimental Q-values for α- as well as cluster-decays. Finally, the empirical estimates of the preformation factors are made for different parent nuclei chosen. It is interesting to find that the empirically evaluated α-preformation probabilities P0α(emp) are almost constant of the order of 10−2 −10−3 for all the parent nuclei studied here. This result means to suggest that a preformation factor P0α is required to match the experimental data for α-decay constant λαExpt, and hence the nuclear structure information is important for α-decay process. Next, the empirically evaluated preformation probabilities P0c(emp) for cluster-decays are found to decrease with the increase in size of clusters emitted from different parents. Also, for α- and cluster-decays from the same parent nucleus, preformation factor P0α(emp) for α-decays is much larger than the P0c(emp) for cluster-decays, such that the ratio P0c(emp)/P0α(emp) is very small, and further decreases with the increase in size of the cluster from 14C to 34Si, as expected. The results obtained for P0c(emp) are within two to three orders of magnitude of the well accepted phenomenological model of Blendowske and Walliser for light clusters. Thus, the important point is that the microscopic RMF formalism, combined with a realistic M3Y+EX interaction, supports the concept of preformation of clusters in nuclei, introduced by Gupta and collaborators in PCM for cluster radioactive decays.