A new interpretation for the wobbling bands in the even-odd Lu isotopes is given within a particle-triaxial rotor semi-classical formalism. While in the previous papers the bands TSD1, TSD2, TSD3 and TSD4 are viewed as the ground, one, two and three phonon wobbling bands, here the corresponding experimental results are described as the ground band with spin equal to I=R+j, for R=0,2,4,...(TSD1), the ground band with I=R+j and R=1,3,5,...(TSD2), the one phonon excitations of TSD2 (TSD3), with the odd proton moving in the orbit $j=i_{13/2}$, and the ground band of I=R+j, with R=1,3,5,... and $j=h_{9/2}$ (TSD4). The moments of inertia (MoI) of the core for the first three bands are the same, and considered to be free parameters. Due to the core polarization effect caused by the particle-core coupling, the MoIs for TSD4 are different. The energies and the e.m. transitions are quantitatively well described. Also, the phase diagram of the odd system is drawn. In the parameter space, one indicates where the points associated with the fitted parameters are located, which is the region where the transversal wobbling mode might be possible, as well as where the wobbling motion is forbidden.
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