  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.
