The ∆I=4 bifurcation in superdeformed bands

The origin of the ∆I=4 staggering effect which has recently been observed in several su-perdeformed bands is discussed. The Hamamoto and Mottelson model, which is based on a phenomenological parametrization of the hamiltonian as a quartic function of angular momentum , is analyzed. A stability of the description with respect to the C 4-symmetry breaking terms is studied. Recently, a puzzling new phenomenon has been observed in few superdeformed rotational sequences. Namely, dynamical moments of inertia of several bands exhibit small regular variations (staggering) as functions of angular momentum. The effect consists in systematic energy displacements of rotational states, which are alternately pushed up and down along the rotational band. One should mention that the effect is of the order of 50 eV, and since the excitation energies of superdeformed bands are of the order of 20 MeV, the observed shifts correspond to a 10 −6 perturbation of the energy levels. This phenomenon was first observed in the superdeformed yrast band of 149 Gd [1]. To date the staggering has also been found in three bands of 194 Hg [2] and in one band of 153 Dy [3]. The characteristic feature is that the bifurcation into two ∆I=4 families appears at a certain (high) rotational frequency, the amplitude of the oscillations increases with spin, and, sometimes, the change of phase in the oscillatory pattern is observed. The bifurcation of the rotational band into the two families of states can be associated with the existence of a higher-order symmetry in superdeformed states. The symmetry results in the 1