Microscopic quantum ideal triaxial rotor model and related self-consistent cranking model: slow-wobbling rotation in Ne-20

Abstract

A microscopic quantum ideal rotor-model intrinsic Hamiltonian for triaxial rotation is derived from the nuclear Schrodinger equation by applying a rotation operator to a deformed nuclear ground state. This Hamiltonian is obtained only when a rigid-flow prescription is used for the three rotation angles in the rotation operator. Using Hartree-Fock variational and second quantization methods, the rotor Hamiltonian is transformed into that of a self-consistent triaxial cranking model (MSCRM-3) with a self-consistent angular-velocity vector, plus residual terms associated with the square of the angular momentum operator and with a two-body interaction. The approximations underlying the conventional cranking model are revealed. For a self-consistent deformed harmonic oscillator potential, the MSCRM-3 Schrodinger equation is transformed into that of a uniaxial cranking model plus local potential-energy cross terms using a rotation of the co-ordinate system. It is shown that uniform rotation is not generally possible. However, for a slow-wobbling rotation, an approximate uniform rotation becomes possible. In this limiting wobbly motion, the potential-energy cross terms are negligibly small, and the uni-axial cranking-model equation is solved analytically using a generalization of the isotropic-velocity-distribution condition of Bohr-Mottelson and Ripka-Blaizot-Kassis. The ground-state rotational-band excitation energy and quadrupole moment are calculated and compared with the measured data in Ne-20 . The results explain the mysterious decrease in the excitation-energy level spacing with increasing angular momentum. The impact of the residual of the square of the angular momentum and a separable quadrupole-quadrupole two-body interaction is studied in the Tamm-Dancoff approximation.