33 research outputs found
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.