The effect of an octupole term in a quadrupole deformed single particlepotential is studied from the classical and quantum mechanical view point.Whereas the problem is nonintegrable, the quantum mechanical spectrumnevertheless shows some shell structure in the superdeformed prolate case forparticular, yet fairly large octupole strengths; for spherical or oblatedeformation the shell structure disappears. This result is associated withclassical periodic orbits which are found by employing the removal ofresonances method; this approximation method allows determination of the shapeof the orbit and of the approximate octupole coupling strength for which itoccurs. The validity of the method is confirmed by solving numerically theclassical equations of motion. The quantum mechanical shell structure isanalysed using the particle number dependence of the fluctuating part of thetotal energy. In accordance with the classical result this dependence turns outto be very similar for a superdeformed prolate potential plus octupole term anda hyperdeformed prolate potential without octupole term. In this way the shellstructure is explained at least for some few hundred levels. The Fouriertransform of the level density further corroborates these findings.
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