232 research outputs found
Giant-dipole Resonance and the Deformation of Hot, Rotating Nuclei
The development of nuclear shapes under the extreme conditions of high spin
and/or temperature is examined. Scaling properties are used to demonstrate
universal properties of both thermal expectation values of nuclear shapes as
well as the minima of the free energy, which can be used to understand the
Jacobi transition. A universal correlation between the width of the giant
dipole resonance and quadrupole deformation is found, providing a novel probe
to measure the nuclear deformation in hot nuclei.Comment: 6 pages including 6 figures. To appear in Phys. Rev. Lett. Revtex
Quantum and semiclassical study of magnetic anti-dots
We study the energy level structure of two-dimensional charged particles in
inhomogeneous magnetic fields. In particular, for magnetic anti-dots the
magnetic field is zero inside the dot and constant outside. Such a device can
be fabricated with present-day technology. We present detailed semiclassical
studies of such magnetic anti-dot systems and provide a comparison with exact
quantum calculations. In the semiclassical approach we apply the Berry-Tabor
formula for the density of states and the Borh-Sommerfeld quantization rules.
In both cases we found good agreement with the exact spectrum in the weak
magnetic field limit. The energy spectrum for a given missing flux quantum is
classified in six possible classes of orbits and summarized in a so-called
phase diagram. We also investigate the current flow patterns of different
quantum states and show the clear correspondence with classical trajectories.Comment: 14 pages, 13 figure
Periodic-Orbit Bifurcations and Superdeformed Shell Structure
We have derived a semiclassical trace formula for the level density of the
three-dimensional spheroidal cavity. To overcome the divergences occurring at
bifurcations and in the spherical limit, the trace integrals over the
action-angle variables were performed using an improved stationary phase
method. The resulting semiclassical level density oscillations and
shell-correction energies are in good agreement with quantum-mechanical
results. We find that the bifurcations of some dominant short periodic orbits
lead to an enhancement of the shell structure for "superdeformed" shapes
related to those known from atomic nuclei.Comment: 4 pages including 3 figure
Uniform approximations for pitchfork bifurcation sequences
In non-integrable Hamiltonian systems with mixed phase space and discrete
symmetries, sequences of pitchfork bifurcations of periodic orbits pave the way
from integrability to chaos. In extending the semiclassical trace formula for
the spectral density, we develop a uniform approximation for the combined
contribution of pitchfork bifurcation pairs. For a two-dimensional double-well
potential and the familiar H\'enon-Heiles potential, we obtain very good
agreement with exact quantum-mechanical calculations. We also consider the
integrable limit of the scenario which corresponds to the bifurcation of a
torus from an isolated periodic orbit. For the separable version of the
H\'enon-Heiles system we give an analytical uniform trace formula, which also
yields the correct harmonic-oscillator SU(2) limit at low energies, and obtain
excellent agreement with the slightly coarse-grained quantum-mechanical density
of states.Comment: LaTeX, 31 pp., 18 figs. Version (v3): correction of several misprint
Semiclassical description of shell effects in finite fermion systems
A short survey of the semiclassical periodic orbit theory, initiated by M.
Gutzwiller and generalized by many other authors, is given. Via so-called
semiclassical trace formmulae, gross-shell effects in bound fermion systems can
be interpreted in terms of a few periodic orbits of the corresponding classical
systems. In integrable systems, these are usually the shortest members of the
most degenerate families or orbits, but in some systems also less degenerate
orbits can determine the gross-shell structure. Applications to nuclei, metal
clusters, semiconductor nanostructures, and trapped dilute atom gases are
discussed.Comment: LaTeX (revteX4) 6 pages; invited talk at Int. Conference "Finite
Fermionic Systems: Nilsson Model 50 Years", Lund, Sweden, June 14-18, 200
Nuclear prolate-shape dominance with the Woods-Saxon potential
We study the prolate-shape predominance of the nuclear ground-state
deformation by calculating the masses of more than two thousand even-even
nuclei using the Strutinsky method, modified by Kruppa, and improved by us. The
influences of the surface thickness of the single-particle potentials, the
strength of the spin-orbit potential, and the pairing correlations are
investigated by varying the parameters of the Woods-Saxon potential and the
pairing interaction. The strong interference between the effects of the surface
thickness and the spin-orbit potential is confirmed to persist for six sets of
the Woods-Saxon potential parameters. The observed behavior of the ratios of
prolate, oblate, and spherical nuclei versus potential parameters are rather
different in different mass regions. It is also found that the ratio of
spherical nuclei increases for weakly bound unstable nuclei. Differences of the
results from the calculations with the Nilsson potential are described in
detail.Comment: 16 pages, 17 figure
Asymmetry and Spin-Orbit Effects in Binding Energy in the Effective Nuclear Surface Approximation
Isoscalar and isovector particle densities are derived analytically by using
the approximation of a sharp edged nucleus within the local energy density
approach with the proton-neutron asymmetry and spin-orbit effects. Equations
for the effective nuclear-surface shapes as collective variables are derived up
to the higher order corrections in the form of the macroscopic boundary
conditions. The analytical expressions for the isoscalar and isovector tension
coefficients of the nuclear surface binding energy and the finite-size
corrections to the stability line are obtained.Comment: Submitted to International Journal of Modern Physics
Semiclassical trace formulae for systems with spin-orbit interactions: successes and limitations of present approaches
We discuss the semiclassical approaches for describing systems with
spin-orbit interactions by Littlejohn and Flynn (1991, 1992), Frisk and Guhr
(1993), and by Bolte and Keppeler (1998, 1999). We use these methods to derive
trace formulae for several two- and three-dimensional model systems, and
exhibit their successes and limitations. We discuss, in particular, also the
mode conversion problem that arises in the strong-coupling limit.Comment: LaTeX2e, 25 pages incl. 9 figures, version 3: final version in print
for J. Phys.
Eigenvalue spectrum for single particle in a spheroidal cavity: A Semiclassical approach
Following the semiclassical formalism of Strutinsky et al., we have obtained
the complete eigenvalue spectrum for a particle enclosed in an infinitely high
spheroidal cavity. Our spheroidal trace formula also reproduces the results of
a spherical billiard in the limit . Inclusion of repetition of each
family of the orbits with reference to the largest one significantly improves
the eigenvalues of sphere and an exact comparison with the quantum mechanical
results is observed upto the second decimal place for . The
contributions of the equatorial, the planar (in the axis of symmetry plane) and
the non-planar(3-Dimensional) orbits are obtained from the same trace formula
by using the appropriate conditions. The resulting eigenvalues compare very
well with the quantum mechanical eigenvalues at normal deformation. It is
interesting that the partial sum of equatorial orbits leads to eigenvalues with
maximum angular momentum projection, while the summing of planar orbits leads
to eigenvalues with except for L=1. The remaining quantum mechanical
eigenvalues are observed to arise from the 3-dimensional(3D) orbits. Very few
spurious eigenvalues arise in these partial sums. This result establishes the
important role of 3D orbits even at normal deformations.Comment: 17 pages, 7 ps figure
Nonperiodic Orbit Sums in Weyl's Expansion for Billiards
Weyl's expansion for the asymptotic mode density of billiards consists of the
area, length, curvature and corner terms. The area term has been associated
with the so-called zero-length orbits. Here closed nonperiodic paths
corresponding to the length and corner terms are constructed.Comment: 8 pages, 2 figure
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