107 research outputs found
Pluralism, Political Creeds, and Competing Ontologies: Faith Leaders as a Resource for Navigating Polarization
Semi-spheroidal Quantum Harmonic Oscillator
A new single-particle shell model is derived by solving the Schr\"odinger
equation for a semi-spheroidal potential well. Only the negative parity states
of the component of the wave function are allowed, so that new magic
numbers are obtained for oblate semi-spheroids, semi-sphere and prolate
semi-spheroids. The semi-spherical magic numbers are identical with those
obtained at the oblate spheroidal superdeformed shape: 2, 6, 14, 26, 44, 68,
100, 140, ... The superdeformed prolate magic numbers of the semi-spheroidal
shape are identical with those obtained at the spherical shape of the
spheroidal harmonic oscillator: 2, 8, 20, 40, 70, 112, 168 ...Comment: 4 pages, 3 figures, 1 tabl
Classical Analysis of Phenomenological Potentials for Metallic Clusters
The classical trajectories of single particle motion in a Wodds-Saxon and a
modified Nilsson potential are studied for axial quadrupole deformation. Both
cases give rise to chaotic behaviour when the deformation in the Woods-Saxon
and the l**2 term in the modified Nilsson potential are turned on. Important
similarities, in particular with regard to the shortest periodic orbits, have
been found.Comment: 9 pages LaTex + 4 figures available via e-mail requests from the
authors, to appear in Phys.Rev.Let
Orbital Magnetic Dipole Mode in Deformed Clusters: A Fully Microscopic Analysis
The orbital M1 collective mode predicted for deformed clusters in a schematic
model is studied in a self-consistent random-phase-approximation approach which
fully exploits the shell structure of the clusters. The microscopic mechanism
of the excitation is clarified and the close correlation with E2 mode
established. The study shows that the M1 strength of the mode is fragmented
over a large energy interval. In spite of that, the fraction remaining at low
energy, well below the overwhelming dipole plasmon resonance, is comparable to
the strength predicted in the schematic model. The importance of this result in
view of future experiments is stressed.Comment: 10 pages, 3 Postscript figures, uses revte
Semiclassical analysis of the lowest-order multipole deformations of simple metal clusters
We use a perturbative semiclassical trace formula to calculate the three
lowest-order multipole (quadrupole \eps_2, octupole \eps_3, and
hexadecapole \eps_4) deformations of simple metal clusters with atoms in their ground states. The self-consistent mean field of the
valence electrons is modeled by an axially deformed cavity and the oscillating
part of the total energy is calculated semiclassically using the shortest
periodic orbits. The average energy is obtained from a liquid-drop model
adjusted to the empirical bulk and surface properties of the sodium metal. We
obtain good qualitative agreement with the results of quantum-mechanical
calculations using Strutinsky's shell-correction method.Comment: LaTeX file (v2) 6 figures, to be published in Phys. Lett.
The 3-Dimensional q-Deformed Harmonic Oscillator and Magic Numbers of Alkali Metal Clusters
Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator
with Uq(3) > SOq(3) symmetry are compared to experimental data for alkali metal
clusters, as well as to theoretical predictions of jellium models, Woods--Saxon
and wine bottle potentials, and to the classification scheme using the 3n+l
pseudo quantum number. The 3-dimensional q-deformed harmonic oscillator
correctly predicts all experimentally observed magic numbers up to 1500 (which
is the expected limit of validity for theories based on the filling of
electronic shells), thus indicating that Uq(3), which is a nonlinear extension
of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic
oscillator, is a good candidate for being the symmetry of systems of alkali
metal clusters.Comment: 13 pages, LaTe
Deformed Harmonic Oscillators for Metal Clusters: Analytic Properties and Supershells
The analytic properties of Nilsson's Modified Oscillator (MO), which was
first introduced in nuclear structure, and of the recently introduced, based on
quantum algebraic techniques, 3-dimensional q-deformed harmonic oscillator
(3-dim q-HO) with Uq(3) > SOq(3) symmetry, which is known to reproduce
correctly in terms of only one parameter the magic numbers of alkali clusters
up to 1500 (the expected limit of validity for theories based on the filling of
electronic shells), are considered. Exact expressions for the total energy of
closed shells are determined and compared among them. Furthermore, the
systematics of the appearance of supershells in the spectra of the two
oscillators is considered, showing that the 3-dim q-HO correctly predicts the
first supershell closure in alkali clusters without use of any extra parameter.Comment: 25 pages LaTeX plus 21 postscript figure
Electronic-structure-induced deformations of liquid metal clusters
Ab initio molecular dynamics is used to study deformations of sodium clusters
at temperatures K. Open-shell Na cluster has two shape
isomers, prolate and oblate, in the liquid state. The deformation is stabilized
by opening a gap at the Fermi level. The closed-shell Na remains magic also
at the liquid state.Comment: REVTex, 11 pages, no figures, figures (2) available upon request
(e-mail to hakkinen at jyfl.jyu.fi), submitted to Phys. Rev.
Electric multipole plasmons in deformed sodium clusters
The random-phase-approximation (RPA) method with separable residual forces
(SRPA) is proposed for the description of multipole electric oscillations of
valence electrons in deformed alkali metal clusters. Both the deformed mean
field and residual interaction are derived self-consistently from the Kohn-Sham
functional. SRPA drastically simplifies the computational effort which is
urgent if not decisive for deformed systems. The method is applied to the
description of dipole, quadrupole and octupole plasmons in deformed sodium
clusters of a moderate size. We demonstrate that, in clusters with the size
N>50, Landau damping successfully competes with deformation splitting and even
becomes decisive in forming the width and gross structure of the dipole
plasmon. Besides, the plasmon is generated by excitations from both ground
state and shape isomers. In such clusters familiar experimental estimates for
deformation splitting of dipole plasmon are useless.Comment: 27 pages, 10 figure
Scissors modes in triaxial metal clusters
We study the scissors mode (orbital M1 excitations) in small Na clusters,
triaxial metal clusters and and the
close-to-spherical , all described in DFT with detailed ionic
background. The scissors modes built on spin-saturated ground and
spin-polarized isomeric states are analyzed in virtue of both macroscopic
collective and microscopic shell-model treatments. It is shown that the mutual
destruction of Coulomb and the exchange-correlation parts of the residual
interaction makes the collective shift small and the net effect can depend on
details of the actual excited state. The crosstalk with dipole and spin-dipole
modes is studied in detail. In particular, a strong crosstalk with spin-dipole
negative-parity mode is found in the case of spin-polarized states. Triaxiality
and ionic structure considerably complicate the scissors response, mainly at
expense of stronger fragmentation of the strength. Nevertheless, even in these
complicated cases the scissors mode is mainly determined by the global
deformation. The detailed ionic structure destroys the spherical symmetry and
can cause finite M1 response (transverse optical mode) even in clusters with
zero global deformation. But its strength turns out to be much smaller than for
the genuine scissors modes in deformed systems.Comment: 17 pages, 5 figure
- …