Rezső G Lovas

MICROSCOPIC THEORY OF CLUSTER RADIOACTIVITY

Recent developments in the dynamical microscopic theories of cluster decay are reviewed with special emphasis on the nuclear structure aspects and physical interpretation of the models. What we call dynamical microscopic theories are those in which the decay width is derived from the nucleonic structures, of the participating nuclei, which are deduced through the solution of their equations of motion. After a brief review of the various expressions for the decay width, we turn to the nuclear-structure aspects of the problem. We thoroughly discuss the treatment of the Pauli effects in models involving macroscopic elements. We settle the long-standing controversy over the cluster-core norm operator that relates microscopic and macroscopic relative-motion wave functions in the transition amplitude. We conclude that the way the norm operator was originally introduced in the mid-1970s is in principle correct. The main part of the paper is a detailed review, in which the approaches considered are categorized according to the structure models used for the parent nucleus. The approaches discussed are the ordinary shell models, the cluster-like shell models and the Bardeen-Cooper-Schrieffer (BCS) approach. By discussing these diverse calculations, it is concluded that the most essential prerequisite for a realistic model of the mother nucleus is that it should correctly describe the cluster correlation in the surface region. This implies that the proton-neutron interaction is indispensable, and the moderate success of ordinary shell models is accounted for by their failure to include both proton-neutron interaction and large enough bases. For the special case of a doubly-closed-shell residual state, cluster-like models are able to cope with this problem, because their bases are more economical, and, for these cases, they provide a fully satisfactory decay theory. The BCS approach, on the other hand, is widely applicable, and is the only one that has been applied to heavy-cluster decay with reasonable success. We point out, however, that the formation amplitude calculated in this model still contains approximations. We explain the success of the BCS theory by showing that, in spite of appearance, it does include proton-neutron interaction, in an effective manner. In discussing the results for the widths, we address the problem of the preformation probability of a cluster-core pair in the parent nucleus. One can be fairly confident that in the ground state of 212Po the amount of core-α-clustering is as high as 20–30%, but, in respect of other cluster-decaying nuclei, the theory is not yet conclusive. We conclude that a satisfactory understanding of heavy-cluster radioactivity requires the application of both more sophisticated cluster models and improved BCS approaches.

Description of nuclei in terms of their substructures

Applications of a microscopic approach of nuclear physics to an α+t+n+n+n+n cluster model of 11Li and to a six-body treatment of 6Li are presented.

Cluster Formation and Decay in a Microscopic Model: The Alpha Decay of 212Po

The purpose of this lecture is to outline a fundamental and apparently satisfactory description of cluster decay. The main title is meant to express this general aim. But the approach has as yet been applied1 only to the α-decay transition leading to the ground state (g.s.) of 208 Pb. Therefore, for simplicity, I shall deal with an α-decay leading to a doubly-closed-shell core, to be denoted by c. To adapt this approach to more complicated cases is straightforward but needs a lot of labour. Nevertheless, since our formulae will not be very detailed, it would only require trivial changes if α were substituted by another cluster. If, however, the daughter were different, then the formulae should be modified to express that the residual state is not a ‘core state’ at the same time, i.e., it contains valence nucleons.

Absolute alpha-decay width of212Po in a mixed shell-and-cluster model

We have reproduced the absolute width of theα decay of the ground state of212Po in a model in which the shell model is combined with a208Pb+α cluster model, and found that the amount of core+α clustering in the parent state is ∼30%.