Tilted-axis wobbling in odd-mass nuclei

A triaxial rotor Hamiltonian with a rigidly aligned high-$j$ quasiparticle is treated by a time-dependent variational principle, using angular momentum coherent states. The resulting classical energy function have three unique critical points in a space of generalized conjugate coordinates, which can minimize the energy for specific ordering of the inertial parameters and a fixed angular momentum state. Due to the symmetry of the problem, there are only two unique solutions, corresponding to wobbling motion around a principal axis and respectively a tilted-axis. The wobbling frequencies are obtained after a quantization procedure and then used to calculate $E2$ and $M1$ transition probabilities. The analytical results are employed in the study of the wobbling excitations of $^{135}$Pr nucleus, which is found to undergo a transition from low angular momentum transverse wobbling around a principal axis toward a tilted-axis wobbling at higher angular momentum.