Solutions for Particle-Rotor and Cranking Models for SinglejConfiguration

The cranking model and the particle-rotor model are solved exactly for the configuration of a single particle with large constant j . The solutions emphasize the importance of the separatrix, which divides the phase space into those regions in which the particle motion is dominated by the deformation and those in which the particle angular momentum precesses around the rotation axis (aligned orbits). The comparison of the cranking and particle-rotor models exhibits major differences for the aligned orbits, if the cranking frequency is identified with the canonically defined rotational frequency. These differences are traced to the occurrence in the particle-rotor model of an oscillatory motion of the rotor superposed on its mean rotational precession.