Theoretical investigation of cluster preformation using empirical formulae and N p N n scheme in trans-lead nuclei

Abstract In the present paper changes of cluster preformation probabilities ( P c ’s) with different quantities like the size of the cluster ( A c ), proton number of the cluster and daughter nuclei ( Z c Z d ), and the decay energy ( Q ) have been studied. Three different formulae are suggested corresponding to each of these variables taking into account of the odd–even effects. The decay half-lives for various cluster emissions have been predicted in the trans-lead region with preformation probabilities using these three formulae. The theoretical estimates are compared with the experimental results and are found to go hand in hand with experimental data. The relation that connects the decay energy ( Q ) with cluster preformation demonstrates better alignment with experimental data compared to the other two models. The cluster preformation probability ( P c ) is also calculated using the N p N n scheme for the effective number of valance particles. The decay half-lives are then calculated with the preformation factors obtained using the N p N n scheme. The comparison with experimental half-lives suggests the applicability of N p N n scheme for the cluster decays in trans-lead region.