Question of γ-softness of a core and possible wobbling in the light of rich experimental data on 119i

Analysis of rich experimental data on four negative parity bands of 119I in frame of the CQPC (Core-Quasiparticle Coupling) model with the h11=2 proton coupled to a collective quadrupole core is presented. Confrontation of results obtained for two kinds of the even–even core: γ-soft and γ-rigid does not show distinct difference. This conclusion confirms hypothesis that a chiral structure in odd–odd nuclei can be equally well-explained with a rigid triaxial core as well with a soft triaxial core. Possible occurrence of a transverse wobbling motion is also briefly discussed.