Classical bifurcation and enhancement of quantum shells: Systematic analysis of reflection-asymmetric deformed oscillator

The correspondence between classical periodic orbits and quantum shell structure is investigated for a reflection-asymmetric deformed oscillator model as a function of quadrupole and octupole deformation parameters. The periodic orbit theory reveals several aspects of quantum level structure for this non-integrable system. Good classical-quantum correspondence is obtained in the Fourier transform of the quantum level density, and the importance of periodic orbit bifurcation is demonstrated. A systematic survey of the local minima of shell energies in the two-dimensional deformation parameter space shows that prominent shell structures do emerge at finite values of the octupole parameter. Correspondences between the regions exhibiting strong shell effects and the classical bifurcation lines are investigated, and the significance of these bifurcations is indicated. (orig.)