Semiclassical treatment of the cranked triaxial rotator

A model Hamiltonian consisting of a triaxial rotator term and a linear combination of angular momentum components is treated both classically and quantum mechanically. In the classical picture one deals with the motion of one degree of freedom which depends on two parameters u, v. The parameters manifold is divided in several phases by separatrices, where the critical points of the Hamilton function, are degenerate. The equations of motion are exactly solved and alternatively treated by a linearization procedure. By quantizing the classical orbits, the semiclassical spectrum is obtained. The quantal Hamiltonian is treated by several methods and the resulting eigenvalues are compared with the semiclassical energies. The present formalism provides a unified description of several extreme models which were widely used in nuclear structure theory. The results can be used for studying the motion of two triaxial ellipsoids around an arbitrarily tilted cranking axis. New features concerning the magnetic as well as the electric properties of nuclear system are expected. (authors)