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 ${}^{161,163,165,167}$Lu, ${}^{167}$Ta ${}^{131}$Cs, ${}^{135}$Pr, ${}^{151}$Eu, ${}^{183}$Au, ${}^{133}$Ba, ${}^{105}$Pd, ${}^{133}$La, ${}^{187}$Au and ${}^{127}$Xe 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 ${}^{133}$La, ${}^{187}$Au (negative parity), ${}^{183}$Au (positive parity) and ${}^{127}$Xe 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.