Current work explores the impact of gamma-softness on partner bands built on the h11/2h11/2 proton-particle-neutron-hole configurations in triaxial odd-odd nuclei. The results of calculations conducted using a core-particle-hole coupling are presented. The model Hamiltonian includes the collective core, the single-particle valence nucleons, and separable quadrupole-quadrupole interactions. The Kerman-Klein method was applied to find eigenstates, which provided a convenient way for exploring core effects. Calculations were made for triaxial cores with various gamma-softness using the General Collective Model keeping the expectation value for the triaxiality parameter fixed at <gamma>=30 deg. The degeneracy in the proton-neutron h11/2h11/2 bands results from the calculations for the gamma-rigid core but is lifted for the gamma-unstable core.
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