Chaos in the low-lying collective states of even-even nuclei: Classical limit

We study the classical dynamical behavior of a family of Hamiltonians in the interacting boson model which describe the low-lying collective states of even-even nuclei. Two measures of classical chaos, the fractional volume of chaotic trajectories and the average largest Lyapunov exponent, are studied as a function of energy, angular momentum, and a parameter which interpolates between rotational and γ-unstable nuclei. Near these two limits the dynamics is regular but in the transition region it becomes chaotic. The results agree with a previous study of quantum chaos in the corresponding quantal model, where spectral and E(2) intensity fluctuations were analyzed. Contrary to most previous numerical studies which were restricted to unrealistic models in two degrees of freedom, the present model is realistic and has five degrees of freedom. The latter correspond to the five quadrupole nuclear shape degrees of freedom.