Abstract
The combined effect of an octupole and hexadecapole term, when added to a strongly deformed axial harmonic oscillator potential, is carefully studied. The problem is nonintegrable, which calls for a thorough classical analysis in order to understand the quantum mechanical results. Shell structure which is found for particular combinations of the deformation parameters are explained in terms of dominant classical periodic orbits. Using the ``removal of resonances'' method as an approximation, explicit expressions in terms of the deformation parameters are obtained for effective winding numbers, which in turn generate the quantum shell structure. A mutual cancellation of the octupole and hexadecapole deformation in prolate superdeformed systems has been discovered. Strongly oblate deformed potentials can yield shell structure only when even higher multipoles are added while prolate potentials can support shell structure for arbitrary higher multipoles.
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