  We develop in this article a microscopic version of the successful
phenomenological hydrodynamic Bohr-Davydov-Faessler-Greiner (BDFG) model for
the collective rotation-vibration motion of a deformed nucleus. The model
derivation is not limited to small oscillation amplitudes. The model
generalizes the author's previous model to include interaction between
collective oscillations in each pair of spatial directions, and to remove many
of the previous-model approximations. To derive the model, the nuclear
Schrodinger equation is canonically transformed to collective coordinates and
then linearized using a constrained variational method. The associated
transformation constraints are imposed on the wavefunction and not on the
particle co-ordinates. This approach yields four self-consistent, time-reversal
invariant, cranking-type Schrodinger equations for the rotation-vibration and
intrinsic motions, and a self-consistency equation. To facilitate comparison
with the BDFG model, simplify the solution of the equations, and gain physical
insight, we restrict in this article the collective oscillations to only two
space dimensions. For harmonic oscillator mean-field potentials, the equations
are then solved in closed forms and applied to the ground-state rotational
bands in some even-even light and rare-earth nuclei. The computed ground-state
rotational band excitation energy, quadrupole moment and electric quadrupole
transition probabilities are found to agree favourably with measured data and
the results from mean-field, Sp(3,R), and SU(3) models.
