295 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
A Particle number conserving shell-correction method
The shell correction method is revisited. Contrary to the traditional
Strutinsky method, the shell energy is evaluated by an averaging over the
number of particles and not over the single-particle energies, which is more
consistent with the definition of the macroscopic energy. In addition, the
smooth background is subtracted before averaging the sum of single-particle
energies, which significantly improves the plateau condition and allows to
apply the method also for nuclei close to the proton or neutron drip lines. A
significant difference between the shell correction energy obtained with the
traditional and the new method is found in particular for highly degenerated
single-particle spectra (as i.e. in magic nuclei) while for deformed nuclei
(where the degeneracy is lifted to a large extent) both estimates are close,
except in the region of super or hyper-deformed states.Comment: 11 pages in LaTeX, 7 figure
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
Connection between the "Strutinsky level density" and the semiclassical level density (published version)
We establish an analytical link between the level density obtained by means
of the Strutinsky averaging method, and the semiclassical level density. This
link occurs only in the so-called "asymptotic limit". It turns out that the
Strutinsky method amounts to an approximation to the semiclassical method. This
approximation contains an unavoidable remainder which constitutes an intrinsic
noise in comparison to the semiclassical method. Thus, the "old" problem of the
dependency of the Strutinsky procedure on the two free smoothing parameters of
the averaging is intimately connected to this noise. On the other hand, we
demonstrate that the noise of the method is small in the average density of
states and in the average energy, whereas it might be non-negligible in the
shell correction itself. In order to improve this method, we give a "rule"
which consists simply of minimizing the relative error made on the average
energy.Comment: 6 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
Closed orbits and spatial density oscillations in the circular billiard
We present a case study for the semiclassical calculation of the oscillations
in the particle and kinetic-energy densities for the two-dimensional circular
billiard. For this system, we can give a complete classification of all closed
periodic and non-periodic orbits. We discuss their bifurcations under variation
of the starting point r and derive analytical expressions for their properties
such as actions, stability determinants, momentum mismatches and Morse indices.
We present semiclassical calculations of the spatial density oscillations using
a recently developed closed-orbit theory [Roccia J and Brack M 2008 Phys. Rev.
Lett. 100 200408], employing standard uniform approximations from perturbation
and bifurcation theory, and test the convergence of the closed-orbit sum.Comment: LaTeX, 42 pp., 17 figures (24 *.eps files, 1 *.tex file); final
version (v3) to be published in J. Phys.
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
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