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Analyzing the Intensities of KâEdge Transitions in X2 Molecules (X = F, Cl, Br) for Use in Ligand KâEdge Xâray Absorption Spectroscopy
Ligand K-edge X-ray absorption spectroscopy (XAS) is regularly used to determine the ligand contribution to metal-ligand bonds. For quantitative studies, the pre-edge transition intensities must be referenced to an intensity standard, and pre-edge intensities obtained from different ligand atoms cannot be compared without standardization due to different cross sections at each absorption edge. In this work, the intensities of the 1s â Ï* transitions in F2, Cl2, and Br2 are analyzed for their use as references for ligand K-edge XAS. We show that the intensities of these transitions are equal to the intensities of the 1s â np transitions in the unbound halogens. This finding is supported by a comparison between the normalized experimental intensities for the molecules and the calculated oscillator strengths for the atoms. These results highlight the potential for these molecules to be used as intensity standards in F, Cl, and Br K-edge XAS experiments
Further functional determinants
Functional determinants for the scalar Laplacian on spherical caps and
slices, flat balls, shells and generalised cylinders are evaluated in two,
three and four dimensions using conformal techniques. Both Dirichlet and Robin
boundary conditions are allowed for. Some effects of non-smooth boundaries are
discussed; in particular the 3-hemiball and the 3-hemishell are considered. The
edge and vertex contributions to the coefficient are examined.Comment: 25 p,JyTex,5 figs. on request
Thermodynamics, Euclidean Gravity and Kaluza-Klein Reduction
The aim of this paper is to find out a correspondence between one-loop
effective action defined by means of path integral in Euclidean gravity
and the free energy obtained by summation over the modes. The analysis is
given for quantum fields on stationary space-times of a general form. For such
problems a convenient procedure of a "Wick rotation" from Euclidean to
Lorentzian theory becomes quite non-trivial implying transition from one real
section of a complexified space-time manifold to another. We formulate
conditions under which and can be connected and establish an explicit
relation of these functionals. Our results are based on the Kaluza-Klein method
which enables one to reduce the problem on a stationary space-time to
equivalent problem on a static space-time in the presence of a gauge
connection. As a by-product, we discover relation between the asymptotic
heat-kernel coefficients of elliptic operators on a dimensional stationary
space-times and the heat-kernel coefficients of a dimensional elliptic
operators with an Abelian gauge connection.Comment: latex file, 22 page
Smeared heat-kernel coefficients on the ball and generalized cone
We consider smeared zeta functions and heat-kernel coefficients on the
bounded, generalized cone in arbitrary dimensions. The specific case of a ball
is analysed in detail and used to restrict the form of the heat-kernel
coefficients on smooth manifolds with boundary. Supplemented by conformal
transformation techniques, it is used to provide an effective scheme for the
calculation of the . As an application, the complete coefficient
is given.Comment: 23 pages, JyTe
Thermodynamics of scalar fields in Kerr's geometry
The one-loop contributions to the entropy for a massive scalar field in a
Kerr black hole are investigated using an approximation of the metric, which,
after a conformal transformation, permits to work in a Rindler-like spacetime.
Of course, as for the Schwarzschild case, the entropy is divergent in the
proximity of the event horizon.Comment: 7 pages, LaTex, (revised version-last section modified
The heat kernel coefficient for oblique boundary conditions
We present a method for the calculation of the heat kernel
coefficient of the heat operator trace for a partial differential operator of
Laplace type on a compact Riemannian manifold with oblique boundary conditions.
Using special case evaluations, restrictions are put on the general form of the
coefficients, which, supplemented by conformal transformation techniques,
allows the entire smeared coefficient to be determined.Comment: 30 pages, LaTe
Multiple reflection expansion and heat kernel coefficients
We propose the multiple reflection expansion as a tool for the calculation of
heat kernel coefficients. As an example, we give the coefficients for a sphere
as a finite sum over reflections, obtaining as a byproduct a relation between
the coefficients for Dirichlet and Neumann boundary conditions. Further, we
calculate the heat kernel coefficients for the most general matching conditions
on the surface of a sphere, including those cases corresponding to the presence
of delta and delta prime background potentials. In the latter case, the
multiple reflection expansion is shown to be non-convergent.Comment: 21 pages, corrected for some misprint
The hybrid spectral problem and Robin boundary conditions
The hybrid spectral problem where the field satisfies Dirichlet conditions
(D) on part of the boundary of the relevant domain and Neumann (N) on the
remainder is discussed in simple terms. A conjecture for the C_1 coefficient is
presented and the conformal determinant on a 2-disc, where the D and N regions
are semi-circles, is derived. Comments on higher coefficients are made.
A hemisphere hybrid problem is introduced that involves Robin boundary
conditions and leads to logarithmic terms in the heat--kernel expansion which
are evaluated explicitly.Comment: 24 pages. Typos and a few factors corrected. Minor comments added.
Substantial Robin additions. Substantial revisio
New times, new politics: history and memory during the final years of the CPGB
This article examines the relationship between collective memory, historical interpretation and political identity. It focuses on the dissolution of the Communist Party of Great Britain (CPGB) as constructed through collective narrative memory, and on Marxist interpretations of history. The divisions within the party and the wider Marxist community, stretching from 1956 until 1991, were often framed around questions of historical interpretation. The events of 1989â1991 created an historical and mnemonic crisis for CPGB members who struggled to reconcile their past identities with their present situation. Unlike the outward-facing revisionism of other political parties, this was an intensely personal affair. The solution for many was to emphasise the need to find new ways to progress socialist aims, without relying on a discredited grand narrative. In contrast, other Communist parties, such as the Communist Party of Britain, which had been established (or âre-establishedâ) in 1988, fared rather better. By adhering to the international party line of renewal and continued struggle, the party was able to hold its narrative together, condemning the excesses of totalitarian regimes, while reaffirming the need for international class struggle
The ground state energy of a spinor field in the background of a finite radius flux tube
We develop a formalism for the calculation of the ground state energy of a
spinor field in the background of a cylindrically symmetric magnetic field. The
energy is expressed in terms of the Jost function of the associated scattering
problem. Uniform asymptotic expansions needed are obtained from the
Lippmann-Schwinger equation. The general results derived are applied to the
background of a finite radius flux tube with a homogeneous magnetic field
inside and the ground state energy is calculated numerically as a function of
the radius and the flux. It turns out to be negative, remaining smaller by a
factor of than the classical energy of the background except for very
small values of the radius which are outside the range of applicability of QED.Comment: 25 pages, 3 figure
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