Analytic view at alpha clustering in even-even heavy nuclei near magic numbers 82 and 126
Abstract.Most studies on the determination of the alpha-decay preformation factor have used decay formulae. The preformation factor is known to contain abundant information on the nuclear structure. The successful determination of the preformation factor through the cluster formation model (CFM) motivates this study to determine the factor for nuclei near the magic numbers and present results in an analytic study based on different comparisons and observations. The difference between preformation factors obtained from CFM and from the decay formula method is significant. The formula method is used for the entire process of alpha decay as a transition between two states, whereas CFM is applied for the initial state of alpha formation. The preformation factor obtained using CFM and clusterization state representation was first compared with that obtained from the decay formula. Results were used to investigate alpha formation in even-even heavy nuclei, including 72 < Z < 92 and 92 < N < 142, near the magic numbers Z = 82 and N = 126. The values of the preformation factor were discussed and explained in detail according to the clusterization state representation to describe the most possible states of ground-state nuclei. The alpha clustering described through CFM is found to be consistent with that described using the decay formula for the open-shell nuclei of N < 126. The presence of more nucleons in the open-shell nuclei results in lower probability for alpha clustering and lower value of the preformation factor. However, few nucleons beyond the closed shell can cause higher probability for alpha clustering and larger value of the preformation factor. The maximum and minimum of the alpha-cluster formation occur in the nucleus of the double-shell closure (with N = 126 and Z = 82 and in the nucleus of two protons and two neutrons more. This formation probability is sensitive to the subshells, leading to the possibility of more clusterization states, including core-cluster, core-cluster1-cluster2, and core-alpha-alpha structures. The cluster states deduced from the formation probability can be used in future studies to extend the Ikeda diagram to the heavy nuclei.