Preformation probability and kinematics of cluster emission yielding Pb-daughters

In the present study,the newly established preformation formula is applied for the first time to study the kinematics of the cluster emission from various radioactive nuclei,especially those that decay to the double shell closure^(208)Pb nucleus and its neighbors as daughters.The recently proposed universal cluster preformation formula has been established based on the concepts that underscore the influence of mass and charge asymmetry(η_(A)andη_(Z)),cluster mass A_(c),and the Q-value,paving the way to quantify the energy contribution during preformation as well as during the tunneling process separately.The cluster-daughter interaction potential is obtained by folding the relativistic mean-field(RMF)densities with the recently developed microscopic R3Y using the NL 3^(*)and the phenomenological M3Y NN potentials to compare their adaptability.The penetration probabilities are calculated from the WKB approximation.With the inclusion of the new preformation probability P_(0),the predicted half-lives of the R3Y and M3Y interactions are in good agreement with the experimental data.Furthermore,a careful inspection reflects slight differences in the decay half-lives,which arise from their respective barrier properties.The P_(0)for systems with double magic shell closure^(208)Pb daughter are found to be an order of≈10^(2)higher than those with neighboring Pb daughter nuclei.By exploring the contributions of the decay energy,the recoil effect of the daughter nucleus is evaluated,in contrast to several other conjectures.Thus,the centrality of the Q-value in the decay process is demonstrated and redefined within the preformed cluster-decay model.Additionally,we have introduced a simple and intuitive set of criteria that governs the estimation of recoil energy in the cluster radioactivity.