Nuclear deformation has played an important role in determining specific phenomena within the area of Nuclear Structure. Triaxial deformation, where the axial symmetry disappears, is an even more elusive phenomenon. Due to the great challenges of measuring triaxial deformation in nuclei directly, it has recently become a hot topic, and an impressive amount of contributions started to give a clearer picture for this physical process. In the last few years, only two clear signatures of triaxial deformation have been identified, namely the wobbling motion (WM) and the chiral symmetry breaking (although it is worth mentioning that WM was theoretically predicted more than 50 years ago). WM is characterized by a precession of the total angular momentum I of a nucleus, combined with an oscillation around a steady position of the projection of I on the quantization axis. The nuclei in which WM appears have a unique energy spectrum, with a rich band structure and they are also characterized by large transition moments of quadrupole type.

In two recent publications, the team successfully described WM for some odd-A Lu isotopes, reproducing the excitation energies and the transition probabilities with a very good accuracy. Some other relevant quantities (like dynamic moments of inertia, alignments) were also quantitatively well described. The formalism is based on a Particle Rotor Model, where an even-even core is coupled to an odd-j nucleon. The odd-j nucleon plays a crucial role in bringing the core in a highly deformed state, and it also stabilizes the entire structure. However, compared to some previous work on the same isotopes, in the present formalism the triaxial band structure of the isotopes has been re-sketched. More precisely, the four triaxial superdeformed (TSD) bands in ¹⁶³Lu are now three ground states (zero-phonon wobbling bands TSD1, TSD2, TSD4) and one excited state (TSD3 is a one-phonon wobbling band). The ground state bands are all obtained variationally, by solving the principle of minimum action. Only TSD3 is obtained by acting with a phonon operator upon the ground band TSD2. Traditionally, TSD1 was determined by solving the variational principle, while the other excited bands where determined through the multi-phonon operators that act on the ground state with different wobbling phonon numbers. Another crucial aspect in the current formalism is that the first two bands in ¹⁶³Lu are actually signature partner bands (with TSD1 being the favored and TSD2 the unfavored). The present calculations are also compared with the previous model from a quantitative standpoint, reaching the conclusion that the band structure reformulation provides a realistic description of the WM.