A phenomenological nuclear cluster model with shell structure

Abstract

A phenomenological nuclear model is outlined which assumes that nucleons are correlated into α-clusters and also have a shell structure. The shell structure is determined by an LS coupling scheme in which the intrinsic spins of the nucleons within an α-cluster interact with each other, but not with the spins of nucleons outside the alpha. In order to apply a quantum-number scheme to α-clusters, it is assumed that the alphas strongly interact and can be described by antisymmetric wave functions which lead to an exclusion principle. A possible quantum-number scheme showing the so-called magic numbers is given. The ground and excited state energies of the nucleons are assumed to depend on the radial and orbital angular momentum quantum numbers of the nucleons. The large binding energy of the α-cluster causes the spatial subgrouping of the nucleons. A semi-empirical binding energy equation in terms of the α-cluster aspect of the model is presented. This equation, which roughly accounts for the nucleons that are not in alphas, is used to interpret the main features of the chart of the nuclides. Some details of nuclear structure are considered in terms of the quantum-number scheme. The magnetic moments on several light nuclei are discussed on the basis of the angular momentum the alphas and extra nucleons might be expected to have. The possibility of other stable clusters, such as deuterons, tritons and 3He, existing in nuclei is also considered. It is shown that deuterons and 3He clusters probably do not occur in stable nuclei. The magnetic moments of 7Li, 19F, 23Na and 27Al indicate that these nuclei have stable triton clusters.