Microscopic investigation of wobbling motion in atomic nuclei using the triaxial projected shell model approach

A systematic investigation of the wobbling band structures observed in odd-mass nuclei of 161,163,165,167Lu, ¹⁶⁷Ta ¹³¹Cs, ¹³⁵Pr, ¹⁵¹Eu, ¹⁸³Au, ¹³³Ba, ¹⁰⁵Pd, ¹³³La, ¹⁸⁷Au and ¹²⁷Xe is performed using the triaxial projected shell model (TPSM) approach. It is demonstrated that all the studied band structures have transverse wobbling mode, except for ¹³³La, ¹⁸⁷Au (negative parity), ¹⁸³Au (positive parity) and ¹²⁷Xe nuclei where the wobbling frequency increases with spin, indicating that the collective motion has a longitudinal character. To elucidate further the wobbling nature of the band structures, electromagnetic transition probabilities have been evaluated and it is observed that inter-band transitions are dominated by $E2$ rather than $M1$ as expected for a typical signature partner band. It is shown that TPSM approach provides a reasonable description of all the measured properties of the studied nuclei.