Perspectives in the theory of nuclear collective motion

This report discusses three different subjects. The first is the development of a generalized version of the VMI (variable moment of inertia) model that ties it to the original form of the IBM (interacting boson model) and provides a possibility of fitting vibrational spectra with generalized vibrational formulas. The second is a suggestion for fitting band crossing calculations of the phenomenological type more completely than has hitherto been done into the framework of the VMI method. The third, which is the most important and far reaching, is the description f a complete mathematical method for the microscopic derivation of the IBM from a conventional shell-model Hamiltonian. In addition to elements already foreseen by previous authors, there is proposed a solution for the most important problem outstanding, not only within the framework of the IBM, but also in all previous work on boson expansion. This is the problem of actually selecting, in a general fashion, the most collective excitations. A criterion is introduced that the subspace constructed from these excitations should possess an average energy that is lower than the rest of the shell model space; the actual implementation of this criterion is explained. 8 tables, 62 references