Ground-gamma band mixing and odd-even staggering in heavy deformed nuclei

It is proposed that the odd-even staggering (OES) in the $\gamma$- bands of heavy deformed nuclei can be reasonably characterized by a discrete approximation of the fourth derivative of the odd-even energy difference as a function of angular momentum $L$. This quantity exhibits a well developed staggering pattern (zigzagging behavior with alternating signs) in rare earth nuclei and actinides with long $\gamma$- bands ($L\geq 10$). It is shown that the OES can be interpreted reasonably as the result of the interaction of the $\gamma$ band with the ground band in the framework of a Vector Boson Model with SU(3) dynamical symmetry. The model energy expression reproduces successfully the staggering pattern in all considered nuclei up to $L=12-13$. The general behavior of the OES effect in rotational regions is studied in terms of the ground--$\gamma$ band-mixing interaction, showing that strong OES effect occurs in regions with strong ground--$\gamma$ band-mixing interaction. The approach used allows a detailed comparison of the OES in $\gamma$ bands with the other kinds of staggering effects in nuclei and diatomic molecules.