Collective Motion in the Nuclear Shell Model. II. The Introduction of Intrinsic Wave-Functions

The wave functions for a number of particles in a degenerate oscillator level, classified in part I according to irreducible representations of the group U₃, are expressed as integrals of the Hill-Wheeler type over intrinsic states. The rotational band structure which appeared in the classification is now understood, since all states of a band are shown to involve the same intrinsic state in the integral. It is possible to use the quantum number K of the intrinsic states as an additional label for the final wave functions, thus distinguishing states which, in the classification of part I, had the same values for all other quantum numbers used. The integral form for the wave functions enables simple expressions to be obtained for the quadrupole moments which resemble those of the rotational model for a permanent deformation.