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.

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.

Small Angle Elastic Scattering of 4.3 MeV Neutrons From U, Bi, and Pb

1973 ◽  
Vol 51 (20) ◽  
pp. 2197-2201 ◽  
Author(s):  
P. W. Martin ◽  
R. McFadden ◽  
B. L. White
Keyword(s):  
Elastic Scattering ◽  
Satisfactory Agreement ◽  
Cross Section ◽  
Cross Sections ◽  
Small Angle ◽  
Differential Cross ◽  
Optical Model ◽  
Differential Cross Sections ◽  
Electromagnetic Interactions ◽  
The Cross

The differential cross sections for 4.3 MeV neutrons elastically scattered from natural samples of U, Bi, and Pb have been measured at laboratory angles of 5, 10, and 15°. In the case of uranium, the data are consistent with calculations based on the nuclear optical model and known electromagnetic interactions. Less satisfactory agreement to the data is obtained in the cross section measurements for lead and bismuth.

scholarly journals Cross sections of electron collisions with noble gases atoms

2021 ◽  
pp. 11-16
Author(s):  
Rusudan Golyatina ◽  
Sergei Maiorov
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Noble Gas ◽  
Empirical Formulas ◽  
Electron Collisions ◽  
Wide Range ◽  
Analytical Formulas ◽  
The Cross ◽  
Approximation Coefficients ◽  
Ionization Cross Sections

Consideration is given to the analysis of data on the cross sections of elastic and inelastic col-lisions of electrons with noble gas atoms. The transport (diffusion) cross section, the excita-tion and ionization cross sections are studied. For the selected sets of experimental and theo-retical data, optimal analytical formulas are found and approximation coefficients are select-ed for them. The obtained semi-empirical formulas allow us to reproduce the cross section values in a wide range of collision energies from 0.001 to 10000 eV with an accuracy of sev-eral percent.

Elastic Scattering of Electrons and Positrons by Screened Nuclei

1966 ◽  
Vol 21 (9) ◽  
pp. 1321-1327 ◽  
Author(s):  
Elmar Zeitler ◽  
Haakon Olsen
Keyword(s):  
Elastic Scattering ◽  
Cross Section ◽  
Cross Sections ◽  
Relativistic Effects ◽  
The Other ◽  
Elastic Electron ◽  
Positron Scattering ◽  
Electrons And Positrons ◽  
Two Factors ◽  
The Cross

Results of calculations of cross sections for elastic electron and positron scattering are given in angular steps of 15 degrees for elements Z=6, 13, 29, 50, 82, and 92 and energies T=0.2, 0.4, 0.7, 1, 2, 4, and 10 MeV. The calculation is based on the separability of the cross section into two factors, one describing screening and the other, spin and relativistic effects. The first factor is obtained by the MOLIÈRE approximation 8. The second factor is taken from a paper by DOGGETT and SPENCER 5. Different screening potentials for Z=29 were applied.

Many-Electron Correlations in the Photoionization of a Nitrogen Atom

1974 ◽  
Vol 52 (4) ◽  
pp. 349-354 ◽  
Author(s):  
N. A. Cherepkov ◽  
L. V. Chernysheva ◽  
V. Radojević ◽  
I. Pavlin
Keyword(s):  
Nitrogen Atom ◽  
Cross Section ◽  
Cross Sections ◽  
Random Phase Approximation ◽  
Random Phase ◽  
Electron Correlations ◽  
Sum Rule ◽  
Hartree Fock ◽  
The Cross ◽  
Good Agreement

Photoionization cross sections for the outer shell of the nitrogen atom ground state are calculated in the single-particle Hartree–Fock approximation and, in order to take into account many-electron correlations, also in the Random Phase Approximation with Exchange (RPAE). To be able to apply the RPAE, its modification for the half-filled shell atom, such as nitrogen atom, is presented. Calculation of length and velocity forms of the cross section in both approximations are compared with the available experimental data, and a good agreement is obtained. It has been found that in the RPAE the influence of many-electron correlations in a nitrogen atom is not great, but it is very important since, in contrast to the Hartree–Fock approximation, it results in the validity of the sum rule and the coincidence of the length and velocity forms of the cross sections, in agreement with the requirement of the general theory. The angular distribution of photoelectrons is also calculated in the RPAE, which has not been measured so far.

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.

POLARIZED AND UNPOLARIZED INCLUSIVE ELECTRON SCATTERING IN NUCLEI AND THE INCLUSIVE NEUTRINO CROSS-SECTION

1995 ◽  
Vol 04 (01) ◽  
pp. 163-179
Author(s):  
S.L. MINTZ ◽  
M. POURKAVIANI
Keyword(s):  
Cross Section ◽  
Electron Scattering ◽  
Cross Sections ◽  
Inelastic Electron ◽  
Nuclear Excitation ◽  
Scattering Cross ◽  
Neutrino Cross Section ◽  
Inclusive Electron ◽  
Scattering Cross Sections ◽  
The Relationship

The unpolarized and parity violating polarized inclusive inelastic electron scattering cross-sections are calculated for incident electrons from threshold to 100 MeV, for the 12C nucleus. The relationship between these cross-sections and the inclusive neutrino cross-section on this same nucleus is discussed. The possibility of using the parity violating polarized electron scattering interaction to obtain the average nuclear excitation is also discussed.

scholarly journals Differential Cross Sections of 9Be(d,p0)10Be, 9Be(d,p1)10Be, 9Be(d,α0)7Li and 9Be(d,α1)7Li reactions

2019 ◽  
Vol 26 ◽  
pp. 151
Author(s):  
P. Tsavalas ◽  
A. Lagoyannis ◽  
K. Mergia ◽  
E. Ntemou ◽  
C. P. Lungu
Keyword(s):  
Elastic Scattering ◽  
Energy Range ◽  
Nuclear Reaction ◽  
Cross Section ◽  
Cross Sections ◽  
Differential Cross ◽  
Areal Density ◽  
Deuteron Energy ◽  
Nuclear Reaction Analysis ◽  
The Cross

In the present work, the cross sections of the 9Be(d,p0)10Be, 9Be(d,p1)10Be,9Be(d,α0)7Li and 9Be(d,α1)7Li in the deuteron energy range Elab= 1 – 2.2 MeV with an energy step of 20 keV and at detection angles between 120o and 170o were measured, suitable for nuclear reaction analysis. A Si3N4film coated with a thin Be layer was used and the cross sections are determined relatively to the cross section of the natSi(d,d)natSi elastic scattering. Additionally, proton and oxygen beam measurements were carried out in order to determine the atomic areal density which is required to determine the cross sections.

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.

Discrepancy of in-medium nucleon–nucleon cross-section in different T-matrix representations

2014 ◽  
Vol 23 (04) ◽  
pp. 1450023 ◽  
Author(s):  
Yong-Zhong Xing ◽  
Xing-Wen Zhao
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Nucleon Nucleon ◽  
Matrix Representations ◽  
Proton Proton ◽  
Hartree Fock ◽  
Wave States ◽  
T Matrix ◽  
The Cross ◽  
Three Body

In this paper, we study the in-medium nucleon–nucleon (NN) cross-section by using the Dirac–Breuckner–Hartree–Fock approximation (DBHF) with T-matrix project technique for determining the nucleon self-energy. By solving Thompson equation for different partial-wave states separately, we find that the discrepancies of nucleon self-energies in various T-matrix project representations are dominated by the channels with smaller angular momentum. Although the cross-section is independent on the project of T-matrix, the medium suppression of the cross-section in various T-matrix representations are apparently different due to the self-consistency of DBHF calculation involving effect mass of nucleon as an iterative parameter. Our results also show that the cross-sections in the complete pseudovector (CPV) choices are larger than those obtained with both DBHF in the pseudoscalar (PS) choice and nonrelativistic Brueckner–Hartree–Fock with three-body force (BHF + 3BF), respectively. Further comparison shows that the neutron–proton (NP) cross-section within DBHF + PV approach, [Formula: see text], is approximately equal to and slightly larger than that evaluated with BHF + 3BF, [Formula: see text], while the neutron–neutron (NN) (or proton–proton (PP)) cross-section given by DBHF + PV method, [Formula: see text], being the closest to the cross-section calculated by using BHF without 3BF in the lower energy region. Additionally, the discrepancies of the in-medium nucleon–nucleon differential cross-section induced by different representations of T-matrix in DBHF are discussed for nuclear matter with different densities.

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