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A microscopic quantum ideal rotor-model Hamiltonian (distinct from that ofBohr's rotational model) is derived for a rotation about a single axis byapplying a dynamic rotation operator to the deformed nuclear ground-statewavefunction. It is shown that the microscopic ideal rotor Hamiltonian isobtained only for a rigid-flow prescription for the rotation angle, with theattendant rigid-flow kinematic moment of inertia. (For the center-of-massmotion, the method predicts the correct mass.) Using Hartree-Fock variationaland second quantization methods, the ideal rotor-model Hamiltonian is reducedto that of a self-consistent cranking model plus residual terms associated withthe square of the angular momentum operator and a two-body interaction. Theapproximations and assumptions underlying the conventional cranking model arerevealed. The resulting nuclear Schrodinger equation, including a residualtwo-body interaction and the residual part of the square of the angularmomentum, is then solved in the Tamm-Dancoff approximation using he eigenstatesof the self-consistent cranking model, with a self-consistent deformed harmonicoscillator potential, as the particle-hole basis states. Good agreement isobtained between the predicted and measured ground-state rotational-bandexcitation energies, including the lowering of the excitation energy withincreasing angular momentum, in Ne-20 when the effects of a 3-D rotation aresimulated in the model.

Microscopic quantum ideal rotor model and related self-consistent cranking model, I: uni-axial rotation case