Supershell Effect and Stability of Classical Periodic Orbits in Reflection-Asymmetric Superdeformed Oscillator

A semiclassical analysis is made of the origin of an undulating pattern in the smoothed level density for a reflection-asymmetric superdeformed oscillator potential. It is suggested that, when the octupole-type deformation increases, an interference effect between two families of periodic orbit with the ratio of periods approximately 2:1 becomes stronger and thus a pronounced ``supershell'' structure appears.Comment: 8 pages, PHYZZX, figures are not included, KUNS119

Normal forms and uniform approximations for bridge orbit bifurcations

We discuss various bifurcation problems in which two isolated periodic orbits exchange periodic ``bridge'' orbit(s) between two successive bifurcations. We propose normal forms which locally describe the corresponding fixed point scenarios on the Poincar\'e surface of section. Uniform approximations for the density of states for an integrable Hamiltonian system with two degrees of freedom are derived and successfully reproduce the numerical quantum-mechanical results.Comment: 25 pages, 18 figures, version published in Journal of Physics A: Mathematical and Theoretica

Semiclassical origin of nuclear ground-state octupole deformations

Background: Ground-state octupole deformations are suggested in nuclei located in the north-east neighbor of the doubly magic nuclei on the nuclear chart (N,Z), such as those in Ba and Ra-Th regions. This systematics has been attributed to the parity mixing of the approximately degenerate Delta l=3 pair of single-particle levels near the Fermi surface. Purpose: Nuclear deformations are governed in most cases by the gross shell structures of the single-particle spectra. I will consider the systematics in octupole deformation from the view point of the gross shell structure, and investigate the mechanism of its manifestation using the semiclassical periodic-orbit theory (POT), which describes the quantum shell effect by means of the periodic orbits (POs) in the corresponding classical system. Methods: To focus on the role of deformation, simplified infinite-well (cavity) and radial power-law potential models are employed taking account of quadrupole and octupole shape degrees of freedom. Nuclear ground-state deformations are investigated over the nuclear chart, and the properties of the deformed shell structures are analyzed by means of the semiclassical POT. Results and conclusions: The systematics in nuclear ground-state octupole deformations are reproduced in simplified mean-field potential models either with or without parity mixing between Delta l=3 pair of levels. The strong octupole deformed shell effect at above the spherical shell closures are explained simply and clearly using the semiclassical POT. They are associated with the local restoration of dynamical symmetry, which enhance the contribution of classical POs to the gross shell effect.Comment: 13 pages, 20 figure

Periodic-orbit approach to the nuclear shell structures with power-law potential models: Bridge orbits and prolate-oblate asymmetry

Deformed shell structures in nuclear mean-field potentials are systematically investigated as functions of deformation and surface diffuseness. As the mean-field model to investigate nuclear shell structures in a wide range of mass numbers, we propose the radial power-law potential model, V \propto r^\alpha, which enables a simple semiclassical analysis by the use of its scaling property. We find that remarkable shell structures emerge at certain combinations of deformation and diffuseness parameters, and they are closely related to the periodic-orbit bifurcations. In particular, significant roles of the "bridge orbit bifurcations" for normal and superdeformed shell structures are pointed out. It is shown that the prolate-oblate asymmetry in deformed shell structures is clearly understood from the contribution of the bridge orbit to the semiclassical level density. The roles of bridge orbit bifurcations in the emergence of superdeformed shell structures are also discussed.Comment: 20 pages, 23 figures, revtex4-1, to appear in Phys. Rev.