672 research outputs found
Structure Factor and Electronic Structure of Compressed Liquid Rubidium
We have applied the quantal hypernetted-chain equations in combination with
the Rosenfeld bridge-functional to calculate the atomic and the electronic
structure of compressed liquid-rubidium under high pressure (0.2, 2.5, 3.9, and
6.1 GPa); the calculated structure factors are in good agreement with
experimental results measured by Tsuji et al. along the melting curve. We found
that the Rb-pseudoatom remains under these high pressures almost unchanged with
respect to the pseudoatom at room pressure; thus, the effective ion-ion
interaction is practically the same for all pressure-values. We observe that
all structure factors calculated for this pressure-variation coincide almost
into a single curve if wavenumbers are scaled in units of the Wigner-Seitz
radius although no corresponding scaling feature is observed in the
effective ion-ion interaction.This scaling property of the structure factors
signifies that the compression in liquid-rubidium is uniform with increasing
pressure; in absolute Q-values this means that the first peak-position ()
of the structure factor increases proportionally to ( being the
specific volume per ion), as was experimentally observed by Tsuji et al.Comment: 18 pages, 11 figure
Nucleus-Electron Model for States Changing from a Liquid Metal to a Plasma and the Saha Equation
We extend the quantal hypernetted-chain (QHNC) method, which has been proved
to yield accurate results for liquid metals, to treat a partially ionized
plasma. In a plasma, the electrons change from a quantum to a classical fluid
gradually with increasing temperature; the QHNC method applied to the electron
gas is in fact able to provide the electron-electron correlation at arbitrary
temperature. As an illustrating example of this approach, we investigate how
liquid rubidium becomes a plasma by increasing the temperature from 0 to 30 eV
at a fixed normal ion-density . The electron-ion
radial distribution function (RDF) in liquid Rb has distinct inner-core and
outer-core parts. Even at a temperature of 1 eV, this clear distinction remains
as a characteristic of a liquid metal. At a temperature of 3 eV, this
distinction disappears, and rubidium becomes a plasma with the ionization 1.21.
The temperature variations of bound levels in each ion and the average
ionization are calculated in Rb plasmas at the same time. Using the
density-functional theory, we also derive the Saha equation applicable even to
a high-density plasma at low temperatures. The QHNC method provides a procedure
to solve this Saha equation with ease by using a recursive formula; the charge
population of differently ionized species are obtained in Rb plasmas at several
temperatures. In this way, it is shown that, with the atomic number as the only
input, the QHNC method produces the average ionization, the electron-ion and
ion-ion RDF's, and the charge population which are consistent with the atomic
structure of each ion for a partially ionized plasma.Comment: 28 pages(TeX) and 11 figures (PS
Lowering and raising operators for the free Meixner class of orthogonal polynomials
We compare some properties of the lowering and raising operators for the
classical and free classes of Meixner polynomials on the real line
Operator ordering in Two-dimensional N=1 supersymmetry with curved manifold
We investigate an operator ordering problem in two-dimensional N=1
supersymmetric model which consists of n real superfields. There arises an
operator ordering problem when the target space is curved. We have to fix the
ordering in quantum operator properly to obtain the correct supersymmetry
algebra. We demonstrate that the super-Poincar\'{e} algebra fixes the correct
operator ordering. We obtain a supercurrent with correct operator ordering and
a central extension of supersymmetry algebra.Comment: 7 page
Probing Ion-Ion and Electron-Ion Correlations in Liquid Metals within the Quantum Hypernetted Chain Approximation
We use the Quantum Hypernetted Chain Approximation (QHNC) to calculate the
ion-ion and electron-ion correlations for liquid metallic Li, Be, Na, Mg, Al,
K, Ca, and Ga. We discuss trends in electron-ion structure factors and radial
distribution functions, and also calculate the free-atom and metallic-atom
form-factors, focusing on how bonding effects affect the interpretation of
X-ray scattering experiments, especially experimental measurements of the
ion-ion structure factor in the liquid metallic phase.Comment: RevTeX, 19 pages, 7 figure
Exact limiting relation between the structure factors in neutron and x-ray scattering
The ratio of the static matter structure factor measured in experiments on
coherent X-ray scattering to the static structure factor measured in
experiments on neutron scattering is considered. It is shown theoretically that
this ratio in the long-wavelength limit is equal to the nucleus charge at
arbitrary thermodynamic parameters of a pure substance (the system of nuclei
and electrons, where interaction between particles is pure Coulomb) in a
disordered equilibrium state. This result is the exact relation of the quantum
statistical mechanics. The experimental verification of this relation can be
done in the long wavelength X-ray and neutron experiments.Comment: 7 pages, no figure
Interaction of photons with plasmas and liquid metals: photoabsorption and scattering
Formulas to describe the photoabsorption and the photon scattering by a
plasma or a liquid metal are derived in a unified manner with each other. It is
shown how the nuclear motion, the free-electron motion and the core-electron
behaviour in each ion in the system determine the structure of photoabsorption
and scattering in an electron-ion mixture. The absorption cross section in the
dipole approximation consists of three terms which represent the absorption
caused by the nuclear motion, the absorption owing to the free-electron motion
producing optical conductivity or inverse Bremsstrahlung, and the absorption
ascribed to the core-electron behaviour in each ion with the Doppler
correction. Also, the photon scattering formula provides an analysis method for
experiments observing the ion-ion dynamical structure factor (DSF), the
electron-electron DSF giving plasma oscillations, and the core-electron DSF
yielding the X-ray Raman (Compton) scattering with a clear definition of the
background scattering for each experiment, in a unified manner. A formula for
anomalous X-ray scattering is also derived for a liquid metal. At the same
time, Thomson scattering in plasma physics is discussed from this general point
of view.Comment: LaTeX file: 18 pages without figur
The smallest eigenvalue of Hankel matrices
Let H_N=(s_{n+m}),n,m\le N denote the Hankel matrix of moments of a positive
measure with moments of any order. We study the large N behaviour of the
smallest eigenvalue lambda_N of H_N. It is proved that lambda_N has exponential
decay to zero for any measure with compact support. For general determinate
moment problems the decay to 0 of lambda_N can be arbitrarily slow or
arbitrarily fast. In the indeterminate case, where lambda_N is known to be
bounded below by a positive constant, we prove that the limit of the n'th
smallest eigenvalue of H_N for N tending to infinity tends rapidly to infinity
with n. The special case of the Stieltjes-Wigert polynomials is discussed
Central factorials under the Kontorovich-Lebedev transform of polynomials
We show that slight modifications of the Kontorovich-Lebedev transform lead
to an automorphism of the vector space of polynomials. This circumstance along
with the Mellin transformation property of the modified Bessel functions
perform the passage of monomials to central factorial polynomials. A special
attention is driven to the polynomial sequences whose KL-transform is the
canonical sequence, which will be fully characterized. Finally, new identities
between the central factorials and the Euler polynomials are found.Comment: also available at http://cmup.fc.up.pt/cmup/ since the 2nd August
201
Electron penetration in the nucleus and its effect on the quadrupole interaction
A series expansion of the interaction between a nucleus and its surrounding
electron distribution provides terms that are well-known in the study of
hyperfine interactions: the familiar quadrupole interaction and the less
familiar hexadecapole interaction. If the penetration of electrons into the
nucleus is taken into account, various corrections to these multipole
interactions appear. The best known one is a scalar correction related to the
isotope shift and the isomer shift. This paper discusses a related tensor
correction, which modifies the quadrupole interaction if electrons penetrate
the nucleus: the quadrupole shift. We describe the mathematical formalism and
provide first-principles calculations of the quadrupole shift for a large set
of solids. Fully relativistic calculations that explicitly take a finite
nucleus into account turn out to be mandatory. Our analysis shows that the
quadrupole shift becomes appreciably large for heavy elements. Implications for
experimental high-precision studies of quadrupole interactions and quadrupole
moment ratios are discussed. A literature review of other small quadrupole-like
effects is presented as well
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