Microscopic investigations of wobbling motion in odd mass nuclei by TPSM

Atomic nuclei can take on asymmetric, triaxial shapes - a phenomenon known as triaxial deformation. One of the clearest signs of such asymmetry is a wobbling motion, similar to a spinning football that wobbles as it rotates. Wobbling has long been studied in heavy, strongly deformed nuclei, but its existence in lighter, normally deformed nuclei has remained unclear. Here we use the triaxial projected shell model to systematically investigate four odd-mass nuclei in the mass-130 region: 127 Xe, 133 Ba, 133 La and 135 Pr. We also present new Triaxial Projected Shall Model (TPSM) calculations for 139 Pm, extending the systematic investigation to include this recently studied wobbling nucleus. Our calculations reproduce the experimental data and reveal that wobbling in these systems can be of two typestransverse or longitudinaldepending on whether the unpaired neutron or proton aligns with the long, short, or medium axis of the nucleus. The same single-particle orbital (h 11/2 ) can give rise to different wobbling behaviours depending on the occupation of the shell. These findings establish normally deformed nuclei as a new testing ground for wobbling excitations and provide a microscopic understanding of how triaxial shapes emerge in nuclear many-body systems. It should be noted that the assignments of two-phonon wobbling bands in these nuclei remain tentative, as definitive electromagnetic transition measurements are still awaited.