Evolution of spectral properties along the O(6)-U(5) transition in the interacting boson model. II. Classical trajectories

We continue our previous study of level dynamics in the [O(6)--U(5)]{⊃}O(5) transition of the interacting boson model [Phys. Rev. C 73, 014306 (2006)] by using the semiclassical theory of spectral fluctuations. We find classical monodromy, related to a singular bundle of orbits with infinite period at energy $E=0$, and bifurcations of numerous periodic orbits for $E>0$. The spectrum of allowed ratios of periods associated with {β} and {γ} vibrations exhibits an abrupt change around zero energy. These findings explain anomalous bunching of quantum states in the E≈0 region, which is responsible for the redistribution of levels between O(6) and U(5) multiplets.