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We develop in this article a microscopic version of the successfulphenomenological hydrodynamic Bohr-Davydov-Faessler-Greiner (BDFG) model forthe collective rotation-vibration motion of a deformed nucleus. The modelderivation is not limited to small oscillation amplitudes. The modelgeneralizes the author's previous model to include interaction betweencollective oscillations in each pair of spatial directions, and to remove manyof the previous-model approximations. To derive the model, the nuclearSchrodinger equation is canonically transformed to collective coordinates andthen linearized using a constrained variational method. The associatedtransformation constraints are imposed on the wavefunction and not on theparticle co-ordinates. This approach yields four self-consistent, time-reversalinvariant, cranking-type Schrodinger equations for the rotation-vibration andintrinsic motions, and a self-consistency equation. To facilitate comparisonwith the BDFG model, simplify the solution of the equations, and gain physicalinsight, we restrict in this article the collective oscillations to only twospace dimensions. For harmonic oscillator mean-field potentials, the equationsare then solved in closed forms and applied to the ground-state rotationalbands in some even-even light and rare-earth nuclei. The computed ground-staterotational band excitation energy, quadrupole moment and electric quadrupoletransition probabilities are found to agree favourably with measured data andthe results from mean-field, Sp(3,R), and SU(3) models.

A microscopic nuclear collective rotation-vibration model: 2D submodel