In an accompanying paper we have described a method that provides a foundation for a quantum theory of large amplitude collective motion. In this method, only the collective degrees of freedom are initially bosonized, i.e., represented by canonical variables. By contrast, in this paper, we describe an alternative method in which all elementary (fermion) density operators defined in the shell model are bosonized. Once again it involves an amalgamation of the Born-Oppenheimer approximation with a version of the Kerman-Klein method. Compared to the alternative it has the advantages of bearing a closer resemblance to the corresponding molecular problem and bringing the role of the Berry potentials clearly into focus. On the other hand, the physical justification for bosonizing the noncollective degrees of freedom is not obvious, and the Pauli principle is only satisfied approximately at every stage of approximation. The method in this paper may also be considered to be an extension to the large amplitude domain of the quantum theory of anharmonic vibrations developed by Marshalek and Weneser. The boson formalism is applied to the problem of the coupling of the giant dipole mode to a quadrupole mode, studied recenty for the effect of Berry potentials by LeTourneux and Vinet.

• Received 29 September 1993

DOI:https://doi.org/10.1103/PhysRevC.49.1439