QUANTUM-THEORY OF LARGE-AMPLITUDE COLLECTIVE MOTION - NATURAL FIT BETWEEN THE BORN-OPPENHEIMER AND KERMAN-KLEIN METHODS

Starting from the shell model, we develop the foundations for a quantum theory of large amplitude collective motion that generalizes and extends some of our earlier work and is otherwise distinct from other methods espoused in the literature. The technical basis of our approach is the amalgamation of the Born-Oppenheimer approximation into the framework of the Kerman-Klein method. The version of the latter that is utilized is one that is applicable to an arbitrary two-body interaction and in which the Pauli principle is satisfied at each level of approximation. In the approximation considered, the one-band or adiabatic approximation, the fit is smooth and seamless, so much so that it is suggested that a multiband approach will be necessary to uncover the Berry potentials. The physics is worked out to the first two orders in the reciprocal of the number of particles participating in the collective motion, comprising the mean-field approximation and the first quantum fluctuations thereto, respectively. It is emphasized that the quantization procedure is integral to the method: there is no ad hoc requantization of a classical limit.