ABSTRACT
In Section 33 a brief survey of the collective model was presented. In that model a deformed shape is defined by a set of collective variables. The spectrum due to this model is that of rotations and vibrations of the deformed shape. It was explained in Section 33 that, in a state with definite values of J and M, the projection of the total angular momentum on the axis of symmetry, defined by the dynamical variables, may have a definite value K. Some valence nucleons may be considered whose coordinates do not take place in the collective variables of the deformed even-even core. Such nucleons may be strongly coupled to the deformed core in which case the projections of their spins on the symmetry axis are good quantum numbers. In the collective model, properties of the combined system are deduced by constructing the nucleon wave functions in the body fixed frame of reference and then transforming states of the combined system to a frame of reference fixed in space. Such an approach is outside the framework of the spherical shell model and will not be followed here. It turns out, however, that it is possible to deal with the problem of nucleons strongly coupled to a rotating core by the usual methods of 924spectroscopy. It is therefore of some interest to derive the results of the collective model for this case by standing on the firmer ground of a frame of reference fixed in space.
