We have studied the (ground-state) cluster radioactive decays within the preformed cluster model (PCM) of Gupta and collaborators [R. K. Gupta, in Proceedings of the 5th International Conference on Nuclear Reaction Mechanisms, Varenna, edited by E. Gadioli (Ricerca Scientifica ed Educazione Permanente, Milano, 1988), p. 416; S. S. Malik and R. K. Gupta, Phys. Rev. C 39, 1992 (1989)]. The relativistic mean-field (RMF) theory is used to obtain the nuclear matter densities for the double folding procedure used to construct the cluster-daughter potential with M3Y nucleon-nucleon interaction including exchange effects. Following the PCM approach, we have deduced empirically the preformation probability ${P_0}^{\mathrm{emp}}$ from the experimental data on both the $\alpha$- and exotic cluster-decays, specifically of parents in the trans-lead region having doubly magic ${}^{208}\mathrm{Pb}$ or its neighboring nuclei as daughters. Interestingly, the RMF-densities-based nuclear potential supports the concept of preformation for both the $\alpha$ and heavier clusters in radioactive nuclei. ${P_0}^{\alpha (\mathrm{emp})}$ for $\alpha$ decays is almost constant ($~$${10}^{-2}$–${10}^{-3}$) for all the parent nuclei considered here, and ${P_0}^{c(\mathrm{emp})}$ for cluster decays of the same parents decrease with the size of clusters emitted from different parents. The results obtained for ${P_0}^{c(\mathrm{emp})}$ are reasonable and are within two to three orders of magnitude of the well-accepted phenomenological model of Blendowske-Walliser for light clusters.

• Received 13 April 2010

DOI:https://doi.org/10.1103/PhysRevC.82.014607