Kerman-Klein-Donau-Frauendorf model for odd-odd nuclei: formal theory

The Kerman-Klein-Donau-Frauendorf (KKDF) model is a linearized version of the Kerman-Klein (equations of motion) formulation of the nuclear many-body problem. In practice, it is a generalization of the standard core-particle coupling model that, like the latter, provides a description of the spectroscopy of odd nuclei in terms of the properties of neighboring even nuclei and of single-particle properties, that are the input parameters of the model. A divers sample of recent applications attest to the usefulness of the model. In this paper, we first present a concise general review of the fundamental equations and properties of the KKDF model. We then derive a corresponding formalism for odd-odd nuclei that relates their properties to those of four neighboring even nuclei, all of which enter if one is to include both multipole and pairing forces. We treat these equations in two ways. In the first we make essential use of the solutions of the neighboring odd nucleus problem, as obtained by the KKDF method. In the second, we relate the properties of the odd-odd nuclei directly to those of the even nuclei. For both choices, we derive equations of motion, normalization conditions, and an expression for transition amplitudes. We also solve the problem of choosing the subspace of physical solutions that arises in an equations of motion approach that includes pairing interactions.