Quadrupole Oscillations as Paradigm of the Chaotic Motion in Nuclei. Part 1

We have presented a complete description of classical dynamics generated by the Hamiltonian of quadrupole nuclear oscillations and identified those peculiarities of quantum dynamics that can be interpreted as quantum manifestations of classical stochasticity. Particular attention has been given to investigation of classical dynamics in the potential energy surface with a few local minima. A new technique is suggested for determination of the critical energy of the transition to chaos. It is simpler than criteria of transition to chaos connected with one or another version of overlap resonances criterion. We have numerically demonstrated that for potential with a localized unstable region motion becomes regular at the high energy again, i.e. transition regularity-chaos-regularity {R - C - R} takes place for these potentials. The variations of statistical properties of energy spectrum in the process of {R - C - R) transition have been studied in detail. We proved that the type of the classical motion is correlated with the structure of the eigenfunctions of highly excited states in the (R - C - R) transition. Shell structure destruction induced by the increase of nonintegrable perturbation was analyzed.