Exactly Solvable Model for the Decay of Superdeformed Nuclei

The history and importance of superdeformation in nuclei is briefly discussed. A simple two-level model is then employed to obtain an elegant expression for the branching ratio for the decay via the E1 process in the normal-deformed band of superdeformed nuclei. From this expression, the spreading width Γ ↓ for superdeformed decay is found to be determined completely by experimentally known quantities. The accuracy of the two-level approximation is verified by considering the effects of other normal-deformed states. Furthermore, by using a statistical model of the energy levels in the normal-deformed well, we can obtain a probabilistic expression for the tunneling matrix element V. Superdeformation is one of the most interesting examples of collective phenomena in atomic nuclei. Since its original experimental observation in 1986, 1 the properties of these high-spin rotational bands have fascinated experimentalists and theoreticians alike. When combined with precisely measured branching ratios and decay rates, a thorough theoretical understanding of the mechanism by which superdeformed (SD) nuclei are formed and then decay into normal-deformed (ND) bands promises to provide a window into nuclear structure unlike any other. One of the major barriers to using SD decay to understand nuclear structure has been that there is no clear way to link the quantities measured in experiment directly with those which might shed light on the internal dynamics of the nucleus. Despite enormous strides made by experimentalists to measure observables precisely, 2,3,4 theorists have failed to reach a consensus on just what to do with these data. Ideally, we require a model which, while accounting for the rich physics of the SD nucleus, is also as simple as possible to allow for easy extraction of quantities of interest to theory. The typical SD nuclear experiment 1,2,3,4 creates nuclei in a high angular momentum state in the SD potential well. These nuclei then lose rotational energy by E2 transitions, eventually reaching a low enough angular momentum that it becomes energetically favorable to decay to states of the same angular momentum in the ND well. As each SD nucleus continues to decay, more strength moves into the energetically preferred ND band rather than continuing down the band of SD states. In practice, most of the decay-out of the SD band happens over the space of only two or three SD states, after which essentially all the strength has moved into the ND band. For a schematic diagram of this process, …