Microscopic quantum ideal rotor model and related self-consistent cranking model, I: uni-axial rotation case
A microscopic quantum ideal rotor-model Hamiltonian (distinct from that of Bohr's rotational model) is derived for a rotation about a single axis by applying a dynamic rotation operator to the deformed nuclear ground-state wavefunction. It is shown that the microscopic ideal rotor Hamiltonian is obtained only for a rigid-flow prescription for the rotation angle, with the attendant rigid-flow kinematic moment of inertia. (For the center-of-mass motion, the method predicts the correct mass.) Using Hartree-Fock variational and second quantization methods, the ideal rotor-model Hamiltonian is reduced to that of a self-consistent cranking model plus residual terms associated with the square of the angular momentum operator and a two-body interaction. The approximations and assumptions underlying the conventional cranking model are revealed. The resulting nuclear Schrodinger equation, including a residual two-body interaction and the residual part of the square of the angular momentum, is then solved in the Tamm-Dancoff approximation using he eigenstates of the self-consistent cranking model, with a self-consistent deformed harmonic oscillator potential, as the particle-hole basis states. Good agreement is obtained between the predicted and measured ground-state rotational-band excitation energies, including the lowering of the excitation energy with increasing angular momentum, in Ne-20 when the effects of a 3-D rotation are simulated in the model.