Collective Motion in Finite Many-Particle Systems. II

This is the second of a series of papers aimed at exploiting a generalized self-consistent approach to the study of collective excited states in finite many-particle systems. It contains: (i) A restatement of the equations of the method with further discussion of the basic approximations involved; (ii) a study, through the medium of the exactly soluble problem of uniform translational motion, of the inherent limitations in accuracy of the method when applied to the "strong-coupling" limit for which it was designed. A mode of approximation which can be made self-consistent is indicated. (iii) This approximation is applied to the problem of rotational motion in a plane. In the further limit in which one assumes the spectrum of the rigid rotator, one regains the results of the self-consistent cranking model. In contrast to previous work, the possibility of removing this limitation is indicated, but remains to be carried through.