GOE-type energy level statistics and regular classical dynamics for rotational nuclei in the interacting boson model

We study the fluctuation properties of $0^{+}$ levels in rotational nuclei using the framework of SU(3) dynamical symmetry of the interacting boson model. Computations of Poincaré sections for SU(3) dynamical symmetry and its breaking confirm the expected relation between dynamical symmetry and classical chaos. On the other hand, the quantal energy level statistics in the realistic case of rotational nuclei is close to Gaussian-orthogonal-ensemble statistics, contrary to expectations. The conjectured relation between energy fluctuations and chaos is approached asymptotically. Several predictions for chaotic behavior of normally deformed and superdeformed rotational nuclei are given.