Theoretical studies in nuclear structure. Final progress report, June 1, 1991--July 31, 1996

The general purview of the project is the theory of collective motion in atomic nuclei. The chief aim is to elucidate the phenomena of (1) anharmonic multiphonon excitations, and (2) collective tilted rotation, both of which are topics of considerable current interest. In the primary stage of an investigation it is often necessary to develop appropriate mathematical tools, as was the case here. In the next stage, the formalism must be tested on simple soluble models. The work described here is mainly concerned with these two stages. The final stage of realistic applications will require more time, manpower and, of course, the necessary funding. Some planning for this last stage has been carried out and anticipated problems axe briefly discussed. As it turns out, both of the above topics can be approached within the unified framework of a theorem that I developed, called the Cranking Bifurcation Theorem (CBT) to be described below. The CBT can be regarded as an outgrowth of the boson expansion method, which provides a general, and, in principal, exact formalism for treating collective excitations. We begin with a brief discussion of the CBT and then continue on to the applications