The effect of self‐consistent potentials on EXAFS analysis

A theory program intended for use with extended X‐ray‐absorption fine structure (EXAFS) spectroscopy and based on the popular FEFF8 is presented. It provides an application programming interface designed to make it easy to integrate high‐quality theory into EXAFS analysis software. This new code is then used to examine the impact of self‐consistent scattering potentials on EXAFS data analysis by methodical testing of theoretical fitting standards against a curated suite of measured EXAFS data. For each data set, the results of a fit are compared using a well characterized structural model and theoretical fitting standards computed both with and without self‐consistent potentials. It is demonstrated that the use of self‐consistent potentials has scant impact on the results of the EXAFS analysis.     

Asymptotic iteration approach to supersymmetric bistable potentials

We examine quasi exactly solvable bistable potentials and their supersymmetric partners within the framework of the asymptotic iteration method (AIM). It is shown that the AIM produces excellent approximate spectra and that some×it is found to be more useful to use the partner potential for computation. We also discuss the direct application of the AIM to the Fokker-Planck equation.     

Electronic structure of ZrTiO4 and HfTiO4: Self-consistent cluster calculations and X-ray spectroscopy studies

Total and partial densities of states of the constituent atoms of ZrTiO₄ and HfTiO₄ titanates have been calculated using a self-consistent cluster method as incorporated in the FEFF8 code. The calculations reveal the similarity of the electronic structure of both titanates and indicate that the valence band of the compounds under consideration is dominated by contributions of O 2p states. These states contribute throughout the whole valence-band region; however their maximum contributions occur in the upper portion of the band. Other significant contributors in the valence-band region are Ti 3d and Zr 4d states in ZrTiO₄ and Ti 3d and Hf 5d states in HfTiO₄. All the above d-like states contribute throughout the whole valence-band region of the titanates; however maximum contributions of the Ti 3d states occur in the upper portion, whilst those of the Zr 4d (Hf 5d) states are in the central portions of the valence band. The FEFF8 calculations render that the bottom of the conduction band of ZrTiO₄ and HfTiO₄ is dominated by contributions of Ti 3d^? states, with also smaller contributions of Zr 4d^?/Hf 5d^? and O 2p^? states. To verify the above FEFF8 data, the X-ray emission bands, representing the energy distributions of mainly O 2p, Ti 3d and Zr 4d states, were measured and compared on a common energy scale. These experimental data are found to be in agreement with the theoretical FEFF8 results for the electronic structure of ZrTiO₄ and HfTiO₄ titanates. Additionally, X-ray photoelectron valence-band and core-level spectra were recorded for the constituent atoms of the titanates under study.     

Electronic structure of metal nanoclusters

The electronic structure and the shape of the K absorption edge for small-sized clusters formed by transition metal atoms (titanium, nickel, and copper) are investigated using the quantum-mechanical multiple scattering method (FEFF8 code) and the molecular mechanics technique. It is shown that the x-ray photoelectron spectra and K x-ray absorption spectra of clusters containing 55 and more atoms are similar to the corresponding experimental spectra of macroscopic samples. The computer simulation of the electronic structure and the shape of the K absorption edge is performed for nanoclusters whose equilibrium geometric shape is determined by the molecular dynamics method.     

Phonon mediated photodetector

Quantum-wells and quantum dots and related semiconductor nanostructures have been widely investigated for infrared devices. Here we propose a new general approach to make use of polar optical phonons in quantum-wells for infrared (IR) and terahertz (THz) detection. As the first example, we show the coupling of phonon and intersubband transition leading to Fano resonance in photocurrent spectra. We investigate the phenomenon experimentally in specially designed GaAs/AlGaAs quantum-well infrared photodetectors. Finally, we discuss the future research and potentials.     

Transforming nonlocality into a frequency dependence: a shortcut to spectroscopy

Measurable spectra are often derived from contractions of many-body Green's functions. One calculates hence more information than needed. Here we present and illustrate an in principle exact approach to construct effective potentials and kernels for the direct calculation of electronic spectra. In particular, a dynamical but local and real potential yields the spectral function needed to describe photoemission. We discuss for model solids the frequency dependence of this "photoemission potential" stemming from the nonlocality of the corresponding self-energy.     

Calculation of quantum correlation spectra using the regression theorem

We present a simple method, based on the quantum regression theorem, to calculate the quantum correlation spectra for two optical beams in the linearized fluctuation regime. As an application, we discuss the dynamical instability, the squeezing spectra and the QND properties of a crossed Kerr-type dispersive model. Received 30 August 1999 and Received in final form 4 July 2000     

Formation of eta'(958)-mesic nuclei and axial UA(1) anomaly at finite density

We discuss the possibility of producing the bound states of the eta'(958) meson in nuclei theoretically. We calculate the formation cross sections of the eta' bound states with the Green function method for the (gamma, p) reaction and discuss the experimental feasibility at photon facilities such as SPring-8. We conclude that we can expect to observe resonance peaks in (gamma, p) spectra for the formation of eta' bound states and we can deduce new information on eta' properties at finite density. These observations are believed to be essential to know the possible mass shift of eta' and deduce new information on the effective restoration of the chiral UA(1) anomaly in the nuclear medium.     

A look at the generalized Darboux transformations for the quasinormal spectra in Schwarzschild black hole perturbation theory: Just how general should it be?

In this article we take a close look at three types of transformations usable in the Schwarzschild black hole perturbation theory: a standard (DT), a binary (BDT) and a generalized (GDT) Darboux transformations. In particular, we discuss the absolutely crucial property of isospectrality of the aforementioned transformations which guarantees that the quasinormal mode (QNM) spectra of potentials, related via the transformation, completely coincide. We demonstrate that, while the first two types of the Darboux transformations (DT and BDT) are indeed isospectral, the situation is wildly different for the GDT: it violates the isospectrality requirement and is therefore only valid for the solutions with just one fixed frequency. Furthermore, it is shown that although in this case the GDT does provide a relationship between two arbitrary potentials (a short-ranged and a long-ranged potentials relationship being just a trivial example), this relationship ends up being completely formal. Finally, we consider frequency-dependent potentials. A new generalization of the Darboux transformation is constructed for them and it is proven (on a concrete example) that such transformations are also not isospectral. In short, we demonstrate how a little, almost incorporeal flaw may become a major problem for an otherwise perfectly admirable goal of mathematical generalization.     

ON FINITE NORMAL SERIES SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH IRREGULAR SINGULARITY

We compute all potentials with the following property: The one-dimensional nonrelativistic Schrödinger equation for these potentials has irregular singular points at infinity and/or zero and is solved by a finite normal series. We restrict to expansion order zero, discuss some properties of the potentials obtained and, as an application, calculate for some given potentials exact solutions and energies. The aim of this paper is to provide a tool for finding exact solutions of the Schrödinger equation for a large class of singular potentials.     

Extended X-ray absorption fine-structure (EXAFS) of a complex oxide structure: a full multiple scattering analysis of the Au L3-edge EXAFS of Au2O3

Crystalline Au₂O₃ was obtained by hydrothermal synthesis at 3000 atm and its extended X-ray absorption fine-structure (EXAFS) at the Au L₃-edge was measured at room temperature. A detailed full multiple scattering (MS) analysis using FEFF8 theory shows that only a small number of scattering paths contribute significantly to the EXAFS of Au₂O₃. Because of the complex unit cell (low local symmetry) of the Au₂O₃ structure, contributions of MS paths are almost negligible. The results indicate that FEFF8 theory provides a good reference for the analysis of Au-O phases.     

Analysis of reflectance data using the Kramers-Kronig Relations

Kramers-Kronig Relations (KKR) are a well-known tool to interpret reflectance spectra by reconstructing the reflected wave's phase from its modulus with the help of a dispersion relation. However, a unscrupulous application is only possible in the case of semiinfinite media at perpendicular incidence.Here the method is generalized to oblique incidence and layered structures. We discuss the KKR's theoretical foundations and their significance for the phase retrieval problem. Firstly, convergence problems occur, in particular in the case of Fabry-Perot-interferences of layered samples. They are removed by a special normalization procedure which is discussed in detail for IR spectra. Since the phase-retrieval procedure is based on a transformation of the un-physical quantity ln R, KKR cannot be applied straightforward. Additional terms have to be considered due to zeroes of the sample's reflection coefficient in the physical half plane. These terms are explained. A method is introduced to evaluate them with the help of few additional data. Finally we discuss an alternative procedure allowing the phase retrieval without further data using physical confinements. As examples the methods are applied to reflectance spectra of BaF₂ and NaCl measured to investigate the materials' multiphonon processes.     

Chemical speciation via X‐ray emission spectra

Since the early days of X‐ray spectrometry, X‐ray emission and fluorescence spectra have been used to investigate chemical speciation, e.g. the dependence on the formal oxidation state. Laboratory wavelength‐dispersive spectrometers have adequate resolution for these measurements. However, almost all studies have employed empirical methods to interpret the spectra. We aim to place such methods on a quantitative basis by means of efficient ab initio calculations of the X‐ray emission line shapes based on a self‐consistent, real‐space Green's function approach, as implemented in the X‐ray spectroscopy code FEFF8.2. Calculations are presented for the phosphorus K‐M_{2, 3}, and the chromium L‐series emission lines for a selection of simple compounds. These lines exhibit changes depending on the oxidation state and on the neighboring atoms in the compounds that can be observed with instruments available in many XRF laboratories. The calculated spectra, as modified by convolution with a model monochromator response function, are compared with measured spectra. Simulated and measured spectra are found to be in reasonable agreement, and show that the approach has the potential to yield quantitative information about the chemical state. Copyright © 2006 John Wiley & Sons, Ltd.     

Coexistence and fluctuations phenomena with Davidson-like potentials in quadrupole-octupole deformed nuclei

The energy spectra of three types of two-dimensional potentials(we will call them‘Davidson-like potentials’(DLPs)),characterized by four minima separated by barriers,are investigated.The predictions for spectra and wave functions are obtained by using the nine-point finite-difference method.For these potentials,with the existence of a single configuration,a transition of spectra,as a function of barrier height,is covered from tunneling splitting modes to fluctuations phenomena,with equal peaks wave functions,crossing to the spectra of purely anharmonic oscillator potentials(AOPs).A different type of phase transition occurs when two(or more)configurations coexist.With the change of the parameters,a transition of spectra is covered from coexistence phenomena of two distinct quantum tunneling modes to fluctuations phenomena,with unequal peaks wave functions,crossing to the spectra of purely AOPs.Using DLPs,a particular application of the coherent quadropole-octupole model to describe energy bands with alternating parity of the nuclei¹⁰⁰Mo,^146,148Nd,^148,150Sm,²²⁰Ra,^220,222Rn,and^220,222Th is presented.The global parametrization of the model for the selected nuclei is achieved.     

Universality in the vibrational spectra of single-component amorphous clusters

We have numerically investigated the vibrational spectra of amorphous single-component clusters for several types of interactions among the particles. For all the potentials we have studied, we find that the density of states can be described, except at the two ends of the spectrum, by the same functional form to a very good approximation, and that the fluctuation properties of the spectra in this central region converge to those of the Gaussian orthogonal ensemble of random matrices with increasing system size. We conjecture that this scenario is true for a broad class of potentials.     

On some classes of exactly-solvable Klein–Gordon equations

In this work we discuss some exactly solvable Klein–Gordon equations. We basically discuss the existence of classes of potentials with different nonrelativistic limits, but which shares the intermediate effective Schroedinger differential equation. We comment about the possible use of relativistic exact solutions as approximations for nonrelativistic inexact potentials.     

Atomic structure of pre‐Guinier–Preston zones in Al alloys

We propose X‐ray absorption (XAS) measurements as a novel approach to determine the atomic structure of pre‐Guinier–Preston zones. These nano‐clusters are formed during very early stages of aging AlCu alloys, immediately after solution heat treatment and quenching. X‐ray absorption near‐edge structure (XANES) spectra were taken from technical aluminum alloys at the copper K edge, revealing the local atomic environment of copper. The spectra of – after solution heat treatment – freshly quenched and of artificially aged alloys differ significantly from each other. We compare the measured XANES spectra with those calculated by the FEFF‐8 code. We show the importance of employing realistic, i.e. relaxed, atomic coordinates around the scattering atom type from ab‐initio calculations with SIESTA. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

     

Quantum graphs with vertices of a preferred orientation

Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the corresponding band spectra of lattices with square and hexagonal elementary cells showing that they depend heavily on the network topology, in particular, on the degrees of the vertices involved.     

Multiwell potentials of endohedral complexes of icosahedral symmetry

We examine multiwell potentials that correspond to the displacements of off-center ions in complexes with icosahedral symmetry (dodecahedrons, icosahedrons, fullerenes, etc.) along symmetry directions (toward vertices, midpoints of edges, and centers of faces). An expression is derived for an effective Hamiltonian, which describes the behavior of endohedral complexes with off-center ions placed in external electric fields of arbitrary strength and orientation. We find the eigenvalues of this Hamiltonian and calculate the intensities of the lines of all possible transitions between tunneling levels. We also predict and analyze the spectra of paraelectric resonances in the absence of an external static electric field (zero-field resonances) and in the presence of such a field. Finally, we provide recommendations for detecting these effects and discuss the specific features of the effects and the possibility of studying them. Zh. éksp. Teor. Fiz. 114, 222–238 (July 1998)