Superdeformed bands with Delta I=4 bifurcation of the odd-A nuclei in the A similar to 190 region

The gamma -ray energy (E-gamma) spectra of the superdeformed (SD) bands of odd-A nuclei in the A similar to 190 mass region are investigated systemati cally. It is found that a DeltaI = 4 bifurcation exists in the SD bands. Wi thin the supersymmetry scheme including many-body interactions and a pertur bation possessing the SO(5) (or SU(5)) symmetry on the rotational symmetry, the E, spectra, dynamical moments of inertia and E, differences delta E-4( gamma) (I) of these bands are evaluated. Quantitative good results are obta ined which show that the scheme is powerful to describe the DeltaI = 4 bifu rcation. The DeltaI = 4 bifurcation may then come from the perturbation hol ding the SO(5) (or SU(5)) symmetry on the rotation. From a microscopic poin t of view, the DeltaI = 4 bifurcation may be a result of the combination of the beta -phonon, gamma -phonon and the rotation.