Abstract
The correspondence of classical dynamical chaos and statistical properties of the energy spectrum has been investigated for the single-particle motion in strongly deformed nuclear potentials with axial symmetry. The properties of the classical and of the quantized system were analyzed for two potentials: the two-center well potential of finite depth and the two-center oscillator shell model. It has been found that in such mean fields the occurrence of fully developed random matrix statistics is a generic feature corresponding to a global instability of classical trajectories. But due to the absence of scaling invariance, for the general case with a mixed phase space a significant energy dependence of the chaotic phase-space volume has been obtained so that the over-all level-spacing distribution cannot be specified by the chaotic volume as a single parameter. The reason for the appearance of chaoticity turns out to be rather complex. Besides the expected important role of large deformations of high multipolarity, including the neck degree of freedom, the spin-orbit part of the nuclear interaction can also be responsible for the occurrence of dynamical chaos.
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We gratefully acknowledge discussions with V.V. Pashkevitch. His computer code and the friendly support of G.R. Tillack made possible the calculation of the level spacing distributions in the twocenter Buck-Put potential. We thank the GSI Darmstadt for the warm hospitality during our stay when parts of this work were completed.