Double Differential Scattering Cross Section Research Articles

Analysis of the time-of-flight neutron scattering cross-section data for light water measured at the SEQUOIA spectrometer, Spallation Neutron Source (SNS)

Thermal neutron scattering cross-section data for light water available in the major nuclear data libraries observes significant differences especially at reactor operating temperatures. During the past few years there has been a renewed interest in reviewing the existing thermal scattering models and generating more accurate and reliable thermal scattering cross sections using existing experimental data and in some cases based on Molecular Dynamics (MD) simulations. There is a need for performing new time-of-flight experiments at high temperatures and pressures, to have a better understanding of the physics involved in the scattering process that could help improve the existing TSL data.Lack of experimental thermal scattering data for light water at high temperatures led to a new measurement campaign within the INSIDER project at the Institut de radioprotection et de sûreté nucléaire (IRSN). Double differential scattering cross section for light water have been measured at the SEQUOIA spectrometer based at the Spallation Neutron Source (SNS), Oak Ridge National Laboratory, United States. Several measurements have been carried out at different temperatures and pressures corresponding to liquid light water. Measurements at five different incident neutron energiesEi(8, 60, 160, 280 and 800 meV) have been carried out to help exploring different regions of the frequency spectrum. This paper presents the analysis of the dynamic structure factor and the derived frequency spectrum of light water. The analysis of the experimental data would provide one with better confidence, the behavior of thermal scattering cross sections for light water at high temperatures, knowledge of which is very important for the design of novel reactors as well as existing pressurized water reactors.

Electron Emission in Ion-Alkali Atoms Collision Process: Three Body Effect

Double differential scattering cross section for emitted electron from ground and excited states when the Ar+18 (75, 85 and 95 Mev/u) scattered off Alkali atom have been calculated within Born approximation following Stolterfoht et al, theoretical model. The emitted electrons from the excited state give large differential cross section comparison with the ground state. Many features of the scattering process are also discussed.

Resonant Compton Scattering of Two Photons by a Multiply Charged Atomic Ion

A pronounced K α1,2 X-ray emission spectrum is theoretically predicted for the resonant inelastic scattering of two photons in the energy region near the 1s shell ionization threshold of a free multiply charged atomic ion. The observed double differential scattering cross section is estimated quantitatively. The results for the Fe16+ ion may be important in interpreting the X-ray emission spectra from galactic clusters, active galactic nuclei, and stars.

Toward a better thermal scattering law of (C5O2H8)n: Inelastic neutron scattering and oClimax + NJOY2016

With the advancements in technology (both experimental and computational) the determination of the“true” experimental phonon spectrum became more accessible. In this work a methodology for producing thermal scattering libraries from the experimental data (namely the DFT + oClimax method) for lucite (C5O2H8)n is discussed. Double differential scattering cross section (DDSCS) experiments were performed at the Spallation Neutron Source of Oak Ridge National Laboratory (SNS ORNL). New scattering kernel evaluations, based on the phonon spectrum for (C5O2H8)n,were created using oClimax and NJOY2016 codes. In order to compare and asses the performance of the newly created library, the experimental setup was simulated using MCNP6.1. Compared to the current ENDF/B-VIII.0, the resulting RPI (C5O2H8)n library improved the calculation of both double differential scattering and total scattering cross sections. A set of criticality benchmarks containing (C5O2H8)n from HEU-MET-THERM resulted in an overall improved calculation of Keff. The DFT + oClimax method is shown to be the most comprehensive method for analysis of moderator materials, due to the fact that it can be verified against all data measured at VISION, ARCS and SEQUOIA neutron spectrometers at SNS ORNL, and experimental total scattering cross section measurements. This method also provides a new technique for calculating any phonon spectrum-related quantities such as scattering law kernel, specific heat capacity, thermal conductivity, etc. for any solid state material.

X-Ray Quadrupole Emission in the Scattering of Two Photons by a Multicharged Atomic Ion

Pronounced spectrally extended quadrupole X-ray emission has been theoretically predicted in resonant inelastic scattering of two photons near the ionization threshold energy of the 1s shell of a free multielectron atom. The observed double differential scattering cross section is estimated quantitatively. The results predicted for the Ar8+ ion possibly concern the problem of identification of X-ray emission spectra near 3.5 keV from galaxies and clusters of galaxies.

Effect of Quadrupole Emission in Scattering of Two Photons by an Atom

A pronounced quadrupole emission effect is theoretically predicted in terms of the contact interaction operator in resonant inelastic scattering of two X-ray photons near the ionization threshold energy of the 1s shell of a free multielectron atom. The observed double differential scattering cross section is estimated quantitatively.

Thermal scattering law of [formula omitted] : Integrating experimental data with DFT calculations

Improvements in determination of the thermal scattering law of moderator materials (measuring, calculating and validating) are important for accurate prediction of neutron thermalization in nuclear systems. In this work a methodology for producing thermal scattering libraries from the experimental data for polyethylene C2H4n is discussed. Double differential scattering cross section (DDSCS) experiments were performed at the Spallation Neutron Source of Oak Ridge National Laboratory (SNS ORNL). New scattering kernel evaluations, based on phonon spectrum for C2H4n, are created using the NJOY2016 code. Two different methods were used: direct and indirect geometry neutron scattering at ARCS and SEQUOIA, and VISION instruments, respectively, where the phonon spectrum was derived from the dynamical structure factor S(Q,ω) obtained from the measured DDSCS. In order to compare and validate the newly created library, the experimental setup was simulated using MCNP6.1. Compared with the current ENDF/B-VII.1, the resulting RPI C2H4n libraries improved both double differential scattering and total scattering cross sections. A set of criticality benchmarks containing C2H4n from HEU-MET-THERM resulted in an overall improved calculation of Keff, although the libraries should be tested against benchmarks more sensitive to C2H4n. The DFT + oClimax method is used and is shown to be most comprehensive method for analysis of moderator materials. The importance of DFT + oClimax method lies in the fact that it can be validated against all data measured at VISION, ARCS and SEQUOIA, and experimental total scattering cross section measurements.

Compton scattering of two x-ray photons by an atom

The process of inelastic nonresonant two x-ray free-electron laser (XFEL) photon Compton scattering by a free atom is theoretically investigated. The object of the study is the He atom. We obtain the absolute values and the shape of the double differential scattering cross section. The quantum effect of creation of ``hot'' scattered photons with maximum energy $2\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{-}{I}_{1s}$ is predicted ($\ensuremath{\hbar}\ensuremath{\omega}$ is the energy of the incident XFEL photon on the atom, and ${I}_{1s}$ is the energy of the ionization threshold of an atomic $1{s}^{2}$ shell).

X-ray-photon Compton scattering by a linear molecule

We formulate a nonrelativistic quantum theory for the nonresonant inelastic scattering process of an x-ray photon by a free linear molecule outside of the impulse approximation framework. We find a strong orientation effect dependent on changes in the schemes of the proposed experiments. Calculations of the absolute values and forms for the double differential scattering cross sections are carried out for the HF molecule and have a predictive character. The presented theory is of a general nature, and its applicability to a particular linear molecule is constrained only by the demand of correctness of nonrelativistic methods for constructing molecular scattering orbitals.

Angular dependence of proton single event multiple-cell upsets in nanometer SRAM

Single event multiple-cell upsets (MCU) increase sharply as the feature size of semiconductor devices shrinks. MCU poses a large challenge on present radiation hardening technology and modeling test technique. Experimental study of the influence of proton incidence angle on single event multiple-cell upsets in 90 nm static random access memory (SRAM) for middle and high energy proton is carried out. The result shows that MCU percentage and multiplicity increase with increasing proton energy, and the MCU topological pattern presents a certain track-orientation characteristic along the trajectories of the incidence ion when the incidence proton is tilted along the X-direction or Y-direction. Single event upset (SEU) cross section has no evident angular dependence. There is some difference in proton MCU cross section between normal incidence and tilt angle incidence only for 30 MeV proton. Angular effect of proton MCU is associated with proton energy. Due to the lower efficiency of Monte-Carlo method in calculating proton MCU, a fast calculation method for cross section, which aims at single event MCU induced by proton nuclear reaction, is adopted. The binary cascade model in Geant4 toolkit serves as event generators in middle on high proton nuclear reaction. In terms of double differential scattering cross section of secondary particle from proton-material spallation reaction, proton MCU cross section is calculated through integration over the entire space of memory cells array. Based on the distribution of secondary particles, those spallation products with the highest linear energy transfer (LET) and longest range are revealed to emit preferentially in the forward direction, which is the root cause why the angular effect of proton-induced MCU exists. The angular dependence of single event MCU in nanometer SRAM depends strongly on proton energy and critical charge. The higher the proton energy is, the wider the angular distribution of secondary particle is, the greater the energy and LET value of the lateral scattered secondary particle is; and so the angular enhancement effect in MCU cross section for lower energy protons is greater than the higher energy protons. MCU cross section is more isotropic with the increase of the proton energy. Angular effect in MCU cross section becomes stronger with the increase of the critical charge for the same energy proton.

Contribution of electric quadrupole transitions to scattering cross section and collected current in a transmission electron microscope

In this paper, the validity of the dipole approximation in the calculation of the double-differential scattering cross section (DDSCS) is investigated. A new expression of the DDSCS is obtained by adding to the classical term associated with the electric dipole transitions two terms taking the electric quadrupole transitions and the interference between dipole and quadrupole transition channels into account. In this study, we restrict to cases where the probed atom site is tetrahedral or octahedral. Moreover, the calculation of the average collected current (ACC) falling into the transition electron microscope collector is carried out by assuming that the incident electron beam is parallel. Then, DDSCS and ACC reduce to a linear combination of five intrinsic components, which only depend on the energy loss. The dominant intrinsic component is associated with the electric dipole transitions, three other intrinsic components are associated with the electric quadrupole transitions, and the last one, which cancels when the probed atom site is an inversion center, is associated with the interferences between dipole and quadrupole transition channels. These intrinsic components are rather hard to calculate, but their weights can be readily evaluated. In the case of the ACC, they essentially depend on the incident beam orientation and the collector aperture. The amplitudes of these weights allow us to evaluate the actual importance of the electric quadrupole transitions. At large collector aperture, the weights of the three quadrupole intrinsic components strongly increase and, thus, the contribution of the electric quadrupole transitions can not be neglected. At smaller collection angles, the importance of the electric quadrupole transitions can be estimated in each particular situation by comparing the amplitudes of the dipole and quadrupole intrinsic components.

The13C(α,n)reaction and its role as a neutron source for thesprocess

The ${}^{13}C(\ensuremath{\alpha},n){}^{16}O$ reaction constitutes the dominant neutron source for the main $s$ process, which operates at a thermal energy of $\mathit{kT}=8$ keV. Since the cross section at stellar energies is very small, the reaction rate cannot be directly determined and has to be extrapolated from cross section results obtained at higher energies. To remove various discrepancies in the normalization of previous data sets and to subsequently improve the reliability of the extrapolation, we performed measurements of the ${}^{13}C(\ensuremath{\alpha},n){}^{16}O$ reaction in the energy range ${E}_{\mathrm{c}.\mathrm{m}.}=320\text{\ensuremath{-}}700$ keV. In addition, the double differential scattering cross section ${}^{13}C(\ensuremath{\alpha},\ensuremath{\alpha}){}^{13}C$ was measured in the energy range ${E}_{\mathrm{lab}}=2.6\text{\ensuremath{-}}6.2$ MeV for 28 angles. These data were used to constrain possible contributions from background resonances for a reliable extrapolation with the multichannel $R$-matrix code SAMMY. As a result, the uncertainties were significantly reduced, and a reaction rate of $(4.6\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{3}$/moles at $\mathit{kT}=8$ keV ($T=0.1\ifmmode\times\else\texttimes\fi{}{10}^{9}$ K) was determined.

Anisotropic relativistic cross sections for inelastic electron scattering, and the magic angle

The knowledge of the inelastic double differential scattering cross section (DDSCS) is of utmost importance for microanalysis in electron energy loss spectrometry (EELS) in the electron microscope and for the investigation of electron energy loss near edge structure (ELNES). Calculations are usually based on a nonrelativistic first-order Born approximation. Relativistic corrections were thought to be important only for primary beam energies much higher than $300\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$. A semirelativistic correction taking into account the relativistic mass change of the probe electron was considered sufficient. We review the relativistic expression of the inelastic double differential scattering cross section (DDSCS) originally given by M\o{}ller. We show that the virtual photon exchange proposed by Fano need not be considered separately. The interference terms between longitudinal and transverse exitations cannot be neglected in anisotropic systems. This explains the surprisingly small magic angle.

Differential electron scattering from positive ions measured by zero-degree ion–atom spectroscopy

Recent developments in quasi-free electron scattering from highly charged ions are reported. Results using a high-efficiency zero-degree Auger projectile spectroscopy setup are presented primarily for collisions of H- and He-like boron beams with H2 targets. A novel technique for the in situ control and determination of the metastable 1s2s3S beam fraction of He-like boron allowed for an accurate determination of absolute double differential scattering cross sections for 180° resonant and non-resonant electron scattering from both ground-(1s2) and mixed-(1s2, 1s2s3S) B3+ states. The observed richly structured B2+ (1s2lnl′) Rydberg series is produced by resonant excitation (RE) from the 1s2 ground state, while the triply excited B2+ (2s2l′2l′′) hollow ionic states are produced by RE from the 1s2s3S metastable state. The consistency of the method was checked by quasi-free electron scattering from H-like B4+ ions giving rise to the 2lnl′ Rydberg series. Differential R-matrix calculations within the electron scattering model for electron–ion scattering from both H-like and ground state He-like boron were found to be in excellent overall agreement. The production of triply excited (2s2l′2l′′) states by RE was also studied for the Z=5–9 isoelectronic sequence. These results convincingly demonstrate that large-angle differential scattering cross section measurements, practically impossible to perform with present day crossed or merged electron–ion beam techniques, are amenable to measurement through high resolution electron spectroscopy of ion–atom collisions, providing some of the most sensitive tests of atomic structure and electron–ion scattering calculations.

Applications of Monte Carlo Simulations of Thermalization Processes to the Nondestructive Assay of Graphite

This work originated because of the need to measure (in situ and nondestructively) the degree of purity of the graphite of the Swiss critical facility Proteus. The comparison between measured and calculated values of the decay constant of a pulse of neutrons λ was the chosen technique. The decay constant (in the absence of fissile materials) depends, mainly, on the purity of the graphite (via the absorption process) and leakage. The leakage factor depends on the thermalization process and the geometry of the system. Because it is very difficult to calculate in complex geometries like the Proteus cavity, Monte Carlo simulations of the behavior of a pulse of neutrons were made with the MCNP code. Despite all the sophistication of MCNP, the ultimate accuracy of the calculations is dependent upon the quality of the nuclear data that describe the thermalization process in the graphite. A recent review of these data shows that very little has changed in the last 30 yr in the ENDF/B evaluation of the double-differential scattering cross section. We decided then to benchmark the current state of the art to compute kinetics experiments in graphite (the MCNP code and the ENDF/B-VI cross-section set) against experimental data and other theoretical results for the analysis of the thermalization problem. Two classes of experiments were analyzed: (a) neutron wave propagation, where the observable is the complex relaxation length, and (b) pulsed neutron decay, where λ is measured as a function of the dimensions of the graphite. Once the bias of the calculational technique was known, it was used to calculate the neutron decay constant of the Proteus cavity as a function of the 10B equivalent impurity concentration. A comparison with pulsed neutron decay experiments made at Proteus allowed the determination of the degree of purity of the graphite. In this last part, we took full advantage of the sophistication of the MCNP code to model many details of the facility quite accurately including room return effects.

Theory of orientation-sensitive near-edge fine-structure core-level spectroscopy

We derive an expression for the double differential scattering cross section for inner-shell excitation of atoms by fast electrons. Using the augmented plane-waves approach for description of the photo electron, we find the inelastic scattering cross section to be a function of energy loss and momentum transfer, which is a priori not proportional to the local symmetry-projected unoccupied density of states. We show the importance of symmetries and choice of coordinate systems, which may necessitate the consideration of cross terms in the expression for the inelastic scattering cross section, coupling different angular momenta of the final state. This has important consequences for the interpretation of energy loss near-edge structure and its counterpart x-ray absorption near edge structure.

Whole-atom Compton scattering of unpolarized photons in the energy region 17.44≤ E≤39.91 keV

Scattering cross sections differential with respect to both the scattering angle and the energy of the scattered photons are derived in the impulse approximation for Al, Cu, Sn and Pb in the energy region 17.44≤ E≤39.91 keV at an angle of 90°. Double differential scattering cross sections are evaluated using nonrelativistic and relativistic expressions based on impulse approximation. The difference between the two expressions is less than 1%, in the important interval P z ≤3 (a.u). With monoenergetic radiation the influence of scattering geometry on the energy broadening is evaluated with respect to the accepted scattering angles and the incident photon energy.

Interference effects in inelastic thickness fringes

We discuss the double differential scattering cross section for atomic inner-shell excitations in crystals. We emphasize interference effects and demonstrate them by means of energy-filtered images of silicon monocrystals under two-beam diffraction conditions. In particular, we measure thickness fringes.

Nondiagonal momentum density of Si by coherent inelastic X-ray scattering

When the coherent superimposition of two (nearly) plane waves is used as the initial photon state of an inelastic X-ray scattering experiment on solids (coherent Compton scattering), information can be obtained about the projection of nondiagonal elements of the one-particle density matrix in momentum space on the scattering vector q, provided the requirements of the impulse approximation are fulfilled. The double differential scattering cross section for this new scattering phenomenon is derived and then subjected to impulse approximation. It is further demonstrated that the standing wave pattern, which on passing the Bragg reflection range is sweeping the atomic sites, yields an appropriate approach to the desired initial photon state for coherent Compton scattering. Experimental coherent Compton spectra from 111 and 220 Bragg reflections are used to extract the corresponding projections of nondiagonal elements of the density matrix. Possible experimental improvements are discussed.

The influence of the orientation averaging on the thermal neutron scattering of the water molecule

Orientation averaging is performed by exact orientation averaging (EOAkappa ) and four approximate methods (two well known and two new) and expressions for the double differential scattering cross sections of thermal neutrons on water molecules are developed. In general, the results obtained by the newly proposed approximate orientation averaging method agree best with the corresponding results obtained by EOAkappa . The biggest discrepancies between the EOAkappa results and results of the approximate methods are obtained using the well known approximate Krieger-Nelkin averaging.