Cluster radioactive decay within the preformed cluster model using relativistic mean-field theory densities

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 P₀ᵉᵐᵖ from the experimental data on 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. Interestingly, the RMF-densities-based nuclear potential supports the concept of preformation for both the α and heavier clusters in radioactive nuclei. P₀^α(emp) for α decays is almost constant ($~$${10}^{{-}2}$--${10}^{{-}3}$) for all the parent nuclei considered here, and ${{P}₀}ᶜ⁽ᵉᵐᵖ⁾$ for cluster decays of the same parents decrease with the size of clusters emitted from different parents. The results obtained for ${{P}₀}ᶜ⁽ᵉᵐᵖ⁾$ are reasonable and are within two to three orders of magnitude of the well-accepted phenomenological model of Blendowske-Walliser for light clusters.