Study of wobbling modes by means of spin coherent state maps

We discuss in depth the interpretation of the quantum states of the model of a triaxial rotor coupled to an odd-particle (PTR). The limitations caused by the discreteness and finiteness of the angular momentum Hilbert space are discussed in detail. We introduce the spin coherent state representation, which directly extracts the classical features from the quantum states. For the triaxial rotor model, the relation to the classical motion of the angular momentum vector is analysed in detail. Two-dimensional plots of the probability distributions of the spin coherent states are used to generalize the classification of the collective excitations of the PTR as transverse and longitudinal wobbling modes based on their topologies. The transition from the transverse to the longitudinal regime with increasing angular momentum is analysed for the first time in full detail, which reveals the appearance of a flip mode in the transition region and that the small-amplitude approximation predicts a too early break-down of the transverse wobbling regime. The relation between the transverse-longitudinal classification and alternative terminology from the literature is clarified.