Rotation-vibration model for the chiral doublet bands and wobbling bands in transitional nuclei

A collective model Hamiltonian incorporating a $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{soft}$ potential is proposed to elucidate phenomena related to triaxiality in transitional systems. The solutions derived from the model built within the core-particle scheme can be approximated using Bessel functions and subsequently applied to describe the exotic high-spin phenomena observed in the $A\ensuremath{\approx}130$ mass region. The results indicate that chiral and wobbling rotations in a $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{soft}$ system may exhibit robustness against $\ensuremath{\beta}$ vibrations, suggesting a collective vibration mechanism for multiple chiral doublet bands and multiple rotation-wobbling bands in triaxial nuclei.