Creation, destruction, and transfer of atomic multipole moments by electron scattering: relativistic treatment1This article is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas.

2011 ◽  
Vol 89 (5) ◽  
pp. 521-531 ◽  
Author(s):  
G. Csanak ◽  
C.J. Fontes ◽  
D.P. Kilcrease ◽  
D.V. Fursa
Keyword(s):  
Elastic Scattering ◽  
Inelastic Scattering ◽  
Cross Section ◽  
Electron Scattering ◽  
Cross Sections ◽  
Matrix Formalism ◽  
Multipole Moments ◽  
Magnetic Sublevel ◽  
Coherence Transfer ◽  
International Colloquium

We have obtained expressions for the creation, destruction, and transfer of atomic multipole moments by electron scattering under relativistic conditions. More specifically, we have obtained separate expressions for different-level processes (inelastic scattering) and for same-level processes (elastic and inelastic scattering). The cross sections for different-level processes are expressed in terms of inelastic magnetic sublevel cross sections, except for the coherence transfer cross section, which is expressed in terms of an angular integral of a product of inelastic magnetic sublevel amplitudes. The same-level cross sections are expressed in terms of the imaginary part of the elastic forward scattering amplitude and in terms of elastic scattering magnetic sublevel cross sections, except for the coherence transfer cross section, which is expressed in terms of the (complex) forward elastic scattering amplitudes and an angular integral of a product of elastic scattering magnetic sublevel amplitudes. If the collisional model supports the optical theorem, then the same-level cross sections can be rewritten in such a form that they are broken up into two parts: an elastic scattering part and an inelastic scattering part. In carrying out this work, we have used the density matrix formalism of Fano and Blum in combination with the electron scattering formalism of Gell-Mann and Goldberger.

Differential cross-section measurements in positron–argon collisions

1996 ◽  
Vol 74 (7-8) ◽  
pp. 505-508 ◽  
Author(s):  
R. M. Finch ◽  
Á. Kövér ◽  
M. Charlton ◽  
G. Laricchia
Keyword(s):  
Elastic Scattering ◽  
Differential Cross Section ◽  
Inelastic Scattering ◽  
Energy Range ◽  
Cross Section ◽  
Cross Sections ◽  
Differential Cross ◽  
Coupling Effect ◽  
Channel Coupling ◽  
Scattering Cross

Differential cross sections for elastic scattering and ionization in positron–argon collisions as a function of energy (40–150 eV) are reported at 60°. Of particular interest is the energy range 55–60 eV, where earlier measurements by the Detroit group found a drop in the elastic-scattering cross section of a factor of 2. This structure has been tentatively attributed to a cross channel-coupling effect with an open inelastic-scattering channel, most likely ionization. Our results indicate that ionization remains an important channel over the same energy range and only begins to decrease at an energy above 60 eV.

Z Dependence of Electron Scattering by Single Atoms into Annular Dark-Field Detectors

2011 ◽  
Vol 17 (6) ◽  
pp. 847-858 ◽  
Author(s):  
Michael M.J. Treacy
Keyword(s):  
Elastic Scattering ◽  
Inelastic Scattering ◽  
Cross Section ◽  
Electron Scattering ◽  
Dark Field ◽  
Single Atom ◽  
Single Atoms ◽  
Annular Dark Field ◽  
Annular Detector ◽  
The Cross

AbstractA simple parameterization is presented for the elastic electron scattering cross sections from single atoms into the annular dark-field (ADF) detector of a scanning transmission electron microscope (STEM). The dependence on atomic number, Z, and inner reciprocal radius of the annular detector, q0, of the cross section σ(Z,q0) is expressed by the empirical relationwhere A(q0) is the cross section for hydrogen (Z = 1), and the detector is assumed to have a large outer reciprocal radius. Using electron elastic scattering factors determined from relativistic Hartree-Fock simulations of the atomic electron charge density, values of the exponent n(Z,q0) are tabulated as a function of Z and q0, for STEM probe sizes of 1.0 and 2.0 Å.Comparison with recently published experimental data for single-atom scattering [Krivanek et al. (2010). Nature464, 571–574] suggests that experimentally measured exponent values are systematically lower than the values predicted for elastic scattering from low-Z atoms. It is proposed that this discrepancy arises from the inelastic scattering contribution to the ADF signal. A simple expression is proposed that corrects the exponent n(Z,q0) for inelastic scattering into the annular detector.

scholarly journals Electron scattering cross-sections for particle transport modeling in a weakly ionized air plasma

2021 ◽  
Vol 51 ◽  
pp. 96-111
Author(s):  
Vasily Sergeevich Zakharov ◽  
Mikhail Evgenievich Zhukovskiy ◽  
Sergey Vasilievich Zakharov ◽  
Mikhail Borisovich Markov
Keyword(s):  
Elastic Scattering ◽  
Cross Section ◽  
Electron Scattering ◽  
Cross Sections ◽  
Electron Interaction ◽  
Inelastic Electron ◽  
Neutral Atoms ◽  
Hartree Fock ◽  
Wide Range ◽  
The Cross

Data on processes of electron scattering on ions and neutral atoms are required in fundamental studies and in applied research in such fields as astro- and laser physics, low density plasma simulations, kinetic modeling etc. Experimental and computational data on elastic and inelastic electron scattering in a wide range of electron energies is available mostly for the electron interaction with neutral atoms, but are very limited for the scattering on ions, notably for elastic processes. In present work the calculational approaches for the cross-section computation of electron elastic and inelastic scattering on neutral atoms and ions are considered. The atomic and ion properties obtained in quantum-statistical Hartree-Fock-Slater model are used in the direct computation of electron elastic scattering and ionization cross-sections by a partial waves method, semiclassical and distorted-wave approximations. Calculated cross-sections for elastic scattering on nitrogen and oxygen atoms and ions, and electron ionisation cross-sections are compared with the available experimental data and widely used approximations and propose consistent results. Considering applicability of Hartree-Fock-Slater model in wide scope of temperatures and densities, such approach to the cross-section calculation can be used in a broad range of energies and ion charges.

A Simulation of Electron Scattering in Metals and its Application for Scanning Electron Microscopy

1990 ◽  
Vol 48 (1) ◽  
pp. 420-421
Author(s):  
Masatoshi Kotera ◽  
Ryoji Ijichi ◽  
Takafumi Fujiwara ◽  
Hiroshi Suga ◽  
David B. Wittry
Keyword(s):  
Elastic Scattering ◽  
Conduction Band ◽  
Cross Section ◽  
Conduction Electron ◽  
Electron Scattering ◽  
Cross Sections ◽  
Electron Ionization ◽  
Plasmon Excitation ◽  
Electron Trajectories ◽  
Scanning Electron

In a recent research, the scanning electron microscope(SEM) has been shown to provide spatial resolution of less than 0.5nm. With the knowledge of the ultimate resolution or the factor which controls the resolution, it is possible to optimize the specimen preparation method and the choice of various electron beam parameters (eg. acceleration voltage etc.) For a precise discussion of the SEM image, it is necessary to take into account not only the signal (electron) production and the propagation in a specimen and its emission from the surface, but also electron trajectories in vacuum toward the detector. However, electron scattering process in the specimen does not depend on the detection system, and the resolution is mainly attributed to the spatial distribution of the electron emission from the specimen surface. Here, we focused on the electron scattering mechanisms in metals and developed a Monte Carlo simulation model of electron trajectories. Also, this simulation is applied to evaluate a compositional contrast in the SEM.In the present study electron interactions with atomic potential, inner-shell electrons, conduction electrons are taken into account. Cross sections calculated by the present model are shown in Fig.1 for [l]elastic scattering, [2]inner-shell (1s, 2s, 2p for Al) electron ionization, [3]conduction electron ionization through non-radiative plasmon decay, and [4] stable plasmon excitation in the conduction band electrons for Al. For the elastic scattering, the Mott cross section is used. For inner-shell electron ionizations by an electron collision, the Gryzinski equation is used. In order to express the plasmon-electron interaction in a free electron gas at the conduction band, the Lindhard treatment is used. This treatment is based on the random phase approximation in the dielectric response function of metals. The cross section is shown in a unit of the inverse mean free path. The cross sections for conduction electron ionization and the plasmon excitation agree with the data of Tung, Ashley, and Ritchie. Cross sections for inner-shell electron ionization, which Tung et al. have derived using the generalized oscillator strength, are also shown in Fig.1 for a comparison.

Electron Scattering in Solids

1990 ◽  
Vol 48 (2) ◽  
pp. 4-5
Author(s):  
Ryuichi Shimizu ◽  
Ze-Jun Ding
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Angular Distribution ◽  
Elastic Scattering ◽  
Electron Scattering ◽  
Cross Sections ◽  
Expansion Method ◽  
Electron Excitation ◽  
Partial Wave Expansion ◽  
Backscattered Electrons

Monte Carlo simulation has been becoming most powerful tool to describe the electron scattering in solids, leading to more comprehensive understanding of the complicated mechanism of generation of various types of signals for microbeam analysis.The present paper proposes a practical model for the Monte Carlo simulation of scattering processes of a penetrating electron and the generation of the slow secondaries in solids. The model is based on the combined use of Gryzinski’s inner-shell electron excitation function and the dielectric function for taking into account the valence electron contribution in inelastic scattering processes, while the cross-sections derived by partial wave expansion method are used for describing elastic scattering processes. An improvement of the use of this elastic scattering cross-section can be seen in the success to describe the anisotropy of angular distribution of elastically backscattered electrons from Au in low energy region, shown in Fig.l. Fig.l(a) shows the elastic cross-sections of 600 eV electron for single Au-atom, clearly indicating that the angular distribution is no more smooth as expected from Rutherford scattering formula, but has the socalled lobes appearing at the large scattering angle.

scholarly journals Saturation effects in SIDIS at very forward rapidities

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
E. Iancu ◽  
A. H. Mueller ◽  
D. N. Triantafyllopoulos ◽  
S. Y. Wei
Keyword(s):  
Inelastic Scattering ◽  
Cross Section ◽  
Cross Sections ◽  
Virtual Photon ◽  
Large Fraction ◽  
Quark Distribution ◽  
High Energy ◽  
Longitudinal Momentum ◽  
Black Disk ◽  
Gluon Saturation

Abstract Using the dipole picture for electron-nucleus deep inelastic scattering at small Bjorken x, we study the effects of gluon saturation in the nuclear target on the cross-section for SIDIS (single inclusive hadron, or jet, production). We argue that the sensitivity of this process to gluon saturation can be enhanced by tagging on a hadron (or jet) which carries a large fraction z ≃ 1 of the longitudinal momentum of the virtual photon. This opens the possibility to study gluon saturation in relatively hard processes, where the virtuality Q2 is (much) larger than the target saturation momentum $$ {Q}_s^2 $$ Q s 2 , but such that z(1 − z)Q2 ≲ $$ {Q}_s^2 $$ Q s 2 . Working in the limit z(1 − z)Q2 ≪ $$ {Q}_s^2 $$ Q s 2 , we predict new phenomena which would signal saturation in the SIDIS cross-section. For sufficiently low transverse momenta k⊥ ≪ Qs of the produced particle, the dominant contribution comes from elastic scattering in the black disk limit, which exposes the unintegrated quark distribution in the virtual photon. For larger momenta k⊥ ≳ Qs, inelastic collisions take the leading role. They explore gluon saturation via multiple scattering, leading to a Gaussian distribution in k⊥ centred around Qs. When z(1 − z)Q2 ≪ Q2, this results in a Cronin peak in the nuclear modification factor (the RpA ratio) at moderate values of x. With decreasing x, this peak is washed out by the high-energy evolution and replaced by nuclear suppression (RpA< 1) up to large momenta k⊥ ≫ Qs. Still for z(1 − z)Q2 ≪ $$ {Q}_s^2 $$ Q s 2 , we also compute SIDIS cross-sections integrated over k⊥. We find that both elastic and inelastic scattering are controlled by the black disk limit, so they yield similar contributions, of zeroth order in the QCD coupling.

scholarly journals A Complete Cross Section Data Set for Electron Scattering by Pyridine: Modelling Electron Transport in the Energy Range 0–100 eV

2020 ◽  
Vol 21 (18) ◽  
pp. 6947
Author(s):  
Filipe Costa ◽  
Ali Traoré-Dubuis ◽  
Lidia Álvarez ◽  
Ana I. Lozano ◽  
Xueguang Ren ◽  
...  
Keyword(s):  
Energy Range ◽  
Cross Section ◽  
Electron Scattering ◽  
Cross Sections ◽  
Transport Model ◽  
Theoretical Data ◽  
Double Differential Cross Section ◽  
Transmission Experiment ◽  
Data Set ◽  
Section Data

Electron scattering cross sections for pyridine in the energy range 0–100 eV, which we previously measured or calculated, have been critically compiled and complemented here with new measurements of electron energy loss spectra and double differential ionization cross sections. Experimental techniques employed in this study include a linear transmission apparatus and a reaction microscope system. To fulfill the transport model requirements, theoretical data have been recalculated within our independent atom model with screening corrected additivity rule and interference effects (IAM-SCAR) method for energies above 10 eV. In addition, results from the R-matrix and Schwinger multichannel with pseudopotential methods, for energies below 15 eV and 20 eV, respectively, are presented here. The reliability of this complete data set has been evaluated by comparing the simulated energy distribution of electrons transmitted through pyridine, with that observed in an electron-gas transmission experiment under magnetic confinement conditions. In addition, our representation of the angular distribution of the inelastically scattered electrons is discussed on the basis of the present double differential cross section experimental results.

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