Semiclassical description of a triaxial rigid rotor

A triaxial rotor Hamiltonian is treated by a time-dependent variational principle, using a coherent state as a trial function. The critical points of the constant energy surface depend on the ordering relations satisfied by the three moments of inertia. All three orderings are considered and to each of them a specific wobbling frequency is derived. The transition between two distinct phases is discussed in terms of a cranking Hamiltonian. Four distinct pairs of complex canonical phase-space coordinates are pointed out. Each of them yields, after quantization, a distinct boson expansion for the angular-momentum components. The separation of the potential energy is treated for one of the four phase-space bases. One of the semiclassical descriptions is used for the yrast state energies of Er-158 and an excellent agreement with experimental data is obtained up to very high angular momentum.