The Born-Oppenheimer theory of nuclear rotations and vibrations

In this paper it is demonstrated that there is a fruitful analogy between nuclear and molecular collective rotations and vibrations. In order to implement this analogy, and to construct the analog of the factorable molecular Born-Oppenheimer trial function, one must transform into a representation, in which the nuclear collective ''position'' operators and the residual intrinsic operators are diagonal. In this representation, the trial function is assumed factorable. Using projection operator techniques, this trial function can be transformed back into a particle coordinate representation, so that conventional many-body techniques can be used. The collective operators are ''chosen'' only to the extent needed to identify the ''type'' of collective process that one intends to describe, by stating their transformation properties under the standard symmetry operations in coordinate-, spin- and isospin space: In the present case, the collective operators form a symmetric, second rank tensor, are isoscalar, and thus describe rotations, and size and quadrupole shape oscillations. A more detailed determination of these operators is based on the dynamical argument of minimal coupling between collective and intrinsic modes of excitation. One then finds that in the harmonic limit, vibrations have frequencies given by RPA type equations, and rotational moments of inertia are determined by self-consistent cranking type prescriptions. (orig.)