Perspectives in the theory of nuclear collective motion

Abstract

This report discusses three different subjects. The first is the development of a generalized version of the VMI (variable moment of inertia) model which ties it to the original form of 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 we consider the most important and far reaching, is the description of 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, we propose 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. We refer to the problem of actually selecting, in a general fashion, the most collective excitations. We introduce a criterion that the subspace constructed from these excitations should possess an average energy which is lower than the rest of the shell model space and explain how this criterion can be implemented in practice.