Nuclear Rotation and Boson Expansions. I

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Abstract
The Beliaev-Zelevinsky method, which represents fermion-pair operators by infinite expansions in exact bosons, is applied to the problem of nuclear rotation. In the harmonic order, which is essentially the random-phase approximation (RPA), the rotation, viewed as infinitesimal, is decoupled from the collective vibrations. The higher orders, however, give rise to various band-mixing terms, which may be interpreted as rotation-vibration and higher-order Coriolis interactions, as well as to vibrational anharmonicities and renormalization of the moment of inertia. A systematic approach is given for extracting these higher-order corrections for the idealized case of a two-dimensional system of interacting particles. Both the Hamiltonian and transition operators are treated. The self-consistent-field approximation is then formulated in the boson picture and applied to the cranking model. The advantage of this formulation is that it allows one to establish the correctness of the higher-order cranking model, which is shown to provide the ground-state-band rotational energies with an error of the order of the small boson-expansion parameter (or the square of this parameter, depending on its definition). The usefulness of the cranking model for obtaining the angular momentum dependence of transition operators is also demonstrated. The Appendix illustrates some of the ideas by way of application to a system of particles interacting through a two-dimensional analog of the quadrupole-quadrupole force.