Periodic orbit bifurcations and local symmetry restorations in exotic-shape nuclear mean fields

The semiclassical origins of the enhancement of shell effects in exotic-shape mean-field potentials are investigated by focusing attention on the roles of the local symmetries associated with the periodic-orbit bifurcations. The deformed shell structures for four types of pure octupole shapes in the nuclear mean-field model having a realistic radial dependence are analyzed. Remarkable shell effects are shown for a large Y32 deformation having tetrahedral symmetry. Much stronger shell effects found in the shape parametrization smoothly connecting the sphere and the tetrahedron are investigated from the view point of the classical-quantum correspondence. The local dynamical symmetries associated with the bridge orbit bifurcations are shown to have significant roles in emergence of the exotic deformed shell structures for certain combinations of the surface diffuseness and the tetrahedral deformation parameters.