Rapidly Rotating Nuclei in the SU3 Model

Rapid rotational motion is studied in the microscopic SU3 model by using the Dynamical Nuclear Field Theory. Assuming small triaxiality, three-dimensional slow rotation is superposed on the fast rotation about a specified body-fixed axis. We use the quantized cranking model. Two basic operators, quadrupole and angular momentum operators, are represented in effective forms. We point out the importance of the higher-order dynamical coupling potentials induced by the constraints imposed on these operators. Effective Hamiltonians are derived in three ways and compared with the exact result. Since the invention of the cranking model by Inglis/> our microscopic understand ing of nuclear collective rotation has much progressed. In this approach, a nucleus deformed axially symmetrically is assumed to rotate about an intrinsic axis (called the x axis) perpendicular to the symmetry axis_ In the case of uniform rotation, we can find stationary states for the Hamiltonian with Coriolis coupling in the rotating frame of reference. We note that a quanta I analogue of the cranking model was proposed by Ripka et al. 2 > However, as shown by simple calculations using a cranked harmonic oscillator (CHO),a> the nucleus loses axial symmetry and deforms triaxially with increasing angular velocity_ Then the rotation axis need not coincide with the x axis_ In this paper we want to study the cranking model in which a three-dimensional rotation is superimposed on the main rotation about the x axis, assuming small triaxiality. Previously, Kinouchi, Kishimoto and Kammuri 4 H> (first two papers are referred to as KKKl and KKK2, respectively) attempted to extend the cranking model in various ways. In order to get some insight into the structure of the motion, they took a simple SUa model for which the group theory gives the exact answers. 7