Inelastic X-ray Scattering Cross Sections Research Articles

Erratum: Electron energy loss and inelastic x-ray scattering cross sections from time-dependent density-functional perturbation theory [Phys. Rev. B88, 064301 (2013)

Erratum: Electron energy loss and inelastic x-ray scattering cross sections from time-dependent density-functional perturbation theory [Phys. Rev. B<b>88</b>, 064301 (2013)

Electron energy loss and inelastic x-ray scattering cross sections from time-dependent density-functional perturbation theory

The Liouville-Lanczos approach to linear-response time-dependent density-functional theory is generalized so as to encompass electron energy loss and inelastic x-ray scattering spectroscopies in periodic solids. The computation of virtual orbitals and the manipulation of large matrices are avoided by adopting a representation of response orbitals borrowed from (time-independent) density functional perturbation theory and a suitable Lanczos recursion scheme. The latter allows the bulk of the numerical work to be performed at any given transferred momentum only once, for a whole extended frequency range. The numerical complexity of the method is thus greatly reduced, making the computation of the loss function over a wide frequency range at any given transferred momentum only slightly more expensive than a single standard ground-state calculation and opening the way to computations for systems of unprecedented size and complexity. Our method is validated on the paradigmatic examples of bulk silicon and aluminum, for which both experimental and theoretical results already exist in the literature.

Observations on the resonant inelastic x-ray scattering cross section in copper oxide compounds

We report properties of the resonant inelastic x-ray scattering (RIXS) cross section in a number of cuprates. We find that the observed spectra have the periodicity of the underlying crystal lattice, that is, the excitations are a function of reduced momentum $\mathbf{q}$ and not the total momentum $\mathbf{Q}=\mathbf{G}+\mathbf{q}$, where $\mathbf{G}$ is a reciprocal lattice vector. Measurements with two different incident photon polarizations show that the line shape and momentum dependence of the observed spectra are independent of the particular state the $4p$ photoelectron resides in the intermediate state. These latter results support theoretical approaches in which the $4p$ is taken to be a spectator in the RIXS process. In addition, a discussion is presented of what might be expected to be generic features of the RIXS cross section with the aid of some crude models, and a comparison is made between RIXS and electron energy loss data for a number of cuprates both at $\mathbf{q}=0$ and at finite $\mathbf{q}$. Taken together, there is a suggestion in the data that RIXS measures an $S(\mathbf{q},\ensuremath{\omega})$-like response.

Inelastic x-ray scattering from phonons under multibeam conditions

We report on an experimental observation of a previously neglected multibeam contribution to the inelastic x-ray scattering cross section. Its manifestation is a substantial modification of the apparent phonon selection rules when two (or more) reciprocal lattice points are simultaneously intercepted by the Ewald sphere. The observed multibeam contributions can be treated semi-quantitatively in the frame of Renninger's 'simplest approach'. A few corollaries, relevant for experimental work on inelastic scattering from phonons, are presented.

Angle resolved resonant inelastic X-ray scattering: intensity and dichroism from 3d transition metals in special geometries

The angular dependence of the resonant inelastic X-ray scattering cross section is studied within the ion-model for 3d metals. A geometrical setup with the incidence direction perpendicular to the magnetic axis and a conical scan of the outgoing radiation is chosen. The total and dichroic intensities have angular asymmetries related to the interference between intermediate states in the process. We show the results of the full calculation of the cross section comparing them with the commonly used fast collision approximation.

Strong coupling corrections in the analysis of x-ray Thomson scattering measurements

We present simplified expressions for the dynamic structure factor, or form factor S(k, ω), which is the quantity describing the inelastic x-ray scattering cross section from a dense plasma or a simple liquid. Our results, based on the random phase approximation (RPA) for the treatment on the charged particle coupling, are compared with analytical expressions for the free electron dynamic structure factor which include effects of strong coupling in both classical and degenerate plasmas. We will show that these modifications introduce minimal corrections to the RPA for typical conditions found in recent non-collective x-ray Thomson scattering experiment on solid density isochorically heated laser plasmas. On the other hand, strong collective scattering may exhibit significant deviations from the RPA. The results shown in this work can be applied to interpreting future x-ray scattering in warm dense plasmas occurring in inertial confinement fusion experiments or for the modelling of solid density matter found in the interior of planets.

Interplay between inelastic X‐ray scattering and ab initio density‐response calculations: Insight into the electronic correlations in aluminum

AbstractInelastic X‐ray scattering (IXS) measurements on Al have been analyzed in conjunction with ab initio, time‐dependent density functional theory (TDDFT) calculations of the electron–hole excitation spectrum. The dynamical structure factor evaluated with use of the many‐body kernel fxc obtained within the adiabatic extension of the local‐density approximation (ALDA) is shown to be in good agreement with the IXS energy‐loss data for energies up to about 20 eV, for momentum transfers up to twice the Fermi wave vector. For larger energy transfers the complex, frequency‐dependent fxc obtained by Devreese and collaborators via dynamical‐exchange decoupling techniques is shown to lead to a description of the IXS data comparable with that of the ALDA. For low energies the ALDA works better, a conclusion with a simple physical interpretation. The analysis of the relative merits of the models for the many‐body interactions is made using IXS cross sections that were obtained in absolute units; to this end, a procedure was introduced which is applicable for arbitrary materials, not just for sp‐bonded Al.

Molecular vibrational spectroscopy by inelastic x-ray scattering: Experimental determination of the absolute vibrational cross section in liquid nitrogen

Inelastic x-ray scattering (IXS) is used to measure the vibrational spectrum of liquid nitrogen at a temperature of 76 K and a pressure of 1 bar as a function of wave vector q in the $1.45\char21{}11.8 {\mathrm{A}}^{\ensuremath{-}1}$ range. The absolute IXS cross section for the vibrational excitation is determined in the explored q range. Its comparison with a theoretical calculation is very satisfactory, and leads to a precise determination of the intramolecular distance and the vibrational root-mean-square displacement. This demonstrates that the IXS technique can provide accurate information on the vibrational dynamics in molecular systems. The peculiarities of IXS with respect to other vibrational spectroscopies are briefly discussed.

Coincidence measurements with X-ray synchrotron sources

The statistical accuracy in coincidence measurements is dependent on the amount of the random coincidences. The expression for the random coincidence count rate in the case of a pulsed synchrotron source is derived from the basic principles. A simple approximative relation between the random-to-true coincidence count rate ratio and the inelastic X-ray scattering cross sections is presented. The different methods to improve the statistical accuracy and to optimize the coincidence measurements are discussed. It is shown that in the case of a synchrotron source the incident flux should sometimes be decreased offering a possibility to use larger detector solid angles. In this way a considerable improvement in the statistical accuracy can be achieved.

Moments of the generalised oscillator strength distribution and total inelastic x-ray scattering cross sections for He and H-

Moments, S( mu ,K), of the generalised oscillator strength distribution are global properties of the Bethe surface. Although S(O,K), S(-1,K) and S( mu ,0) have been thoroughly studied, little is known about the other moments for K not=0. This paper describes high accuracy calculations of S(1,K) and S(2,K) for He and H-. Electron correlation effects are found to be important. A comparison of the theoretical results for helium with experimental ones suggests that there are large errors in the latter. Asymptotic forms that should be useful for more complex systems are presented. The moments are used to calculate total inelastic X-ray scattering cross sections differential with respect to the solid angle by Bonham's new method. The Bonham cross sections differ from the usual Waller-Hartree cross sections at large angles, and the differences increase with the frequency of the incident X-ray. The inelastic cross sections are combined with elastic ones to permit comparison with the total cross sections for scattering of 6 keV photons from helium measured by Ice et al. (1978) with synchrotron radiation. The calculations which include Bonham inelastic cross sections are in better agreement with experiment than the Waller-Hartree results. However, higher accuracy experiments are needed to definitively exclude the Waller-Hartree cross sections.

Moments of the generalised oscillator strength distribution and total inelastic X-ray scattering cross sections for He and H-

Moments, S( mu ,K), of the generalised oscillator strength distribution are global properties of the Bethe surface. Although S(O,K), S(-1,K) and S( mu ,0) have been thoroughly studied, little is known about the other moments for K not=0. This paper describes high accuracy calculations of S(1,K) and S(2,K) for He and H-. Electron correlation effects are found to be important. A comparison of the theoretical results for helium with experimental ones suggests that there are large errors in the latter. Asymptotic forms that should be useful for more complex systems are presented. The moments are used to calculate total inelastic X-ray scattering cross sections differential with respect to the solid angle by Bonham's new method. The Bonham cross sections differ from the usual Waller-Hartree cross sections at large angles, and the differences increase with the frequency of the incident X-ray. The inelastic cross sections are combined with elastic ones to permit comparison with the total cross sections for scattering of 6 keV photons from helium measured by Ice et al. (1978) with synchrotron radiation. The calculations which include Bonham inelastic cross sections are in better agreement with experiment than the Waller-Hartree results. However, higher accuracy experiments are needed to definitively exclude the Waller-Hartree cross sections.

Inelastic X-ray scattering cross sections of Ne

Inelastic X-ray differential scattering cross sections of Ne have been computed to compare the effect of three non-relativistic approximations: Waller-Hartree, impulse and excited state. The same Hartree-Slater wavefunctions were employed throughout, and momentum transfer 0.1<or=K/4 pi <or=1.5 AA-1 was included. For momentum transfer below 0.5 AA-1 the Waller-Hartree and excited-state results were found to agree within 4%, whereas the impulse approximation results are up to 300% higher. The Compton profiles of the individual atomic shells were computed in the excited-state approximation for three values of incident X-ray energy and are found to vary in height and shape with energy and scattering angle, in contrast with the constant profiles predicted by the impulse approximation. Results of theoretical ratios of X-ray inelastic and elastic scattering cross sections are compared with data from an experiment performed with synchrotron radiation. Waller-Hartree and excited-state results agree fairly well with experiment.