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Electron Scattering in Gases –from Cross Sections to Plasma Modeling

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A special issue of Atoms (ISSN 2218-2004).

Deadline for manuscript submissions: closed (15 November 2021) | Viewed by 40824

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Special Issue Editor

Prof. Dr. Grzegorz Piotr Karwasz

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Guest Editor

Institute of Physics, Uniwersytet Mikołaja Kopernika w Toruniu, 87 100 Torun, Poland
Interests: atomic physics; spectroscopy; electron and positron scattering; solid state physics; didactics of sciences

Special Issue Information

Dear Colleagues,

The first experiments on electron scattering were completed before the “official” discovery of this particle by J. J. Thomson. In spite of this, our knowledge of cross sections is still far from complete.

More recent experiments had some unexpected results, like selective fragmentation of DNA constituents by low-energy electrons, or “reverse” phenomena, i.e., synthesis of simple amino acids from inorganic precursors, triggered by slow electrons. The most recent need for cross sections comes from modeling plasmas for industrial and thermonuclear applications, and atmospheres of solar and extra-solar planets.

Both fundamental research (experiments, theory, reviews) and applications of electron-scattering cross sections in various processes are welcome.

Prof. Grzegorz Piotr Karwasz
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Atoms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1500 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (19 papers)

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Editorial

Jump to: Research, Review

6 pages, 230 KiB

Open AccessEditorial

“Atoms” Special Issue (Electron Scattering in Gases—From Cross Sections to Plasma Modeling)

by Grzegorz P. Karwasz

Atoms 2022, 10(2), 54; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms10020054 - 27 May 2022

Cited by 1 | Viewed by 1468

Abstract

Experimental studies of electron scattering in gases, under the name of “cathode rays”, started before the “official” discovery of the electron by J [...] Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

Research

Jump to: Editorial, Review

7 pages, 595 KiB

Open AccessArticle

Electron Impact Ionization of Metastable States of Diatomic Molecules

by Annarita Laricchiuta, Roberto Celiberto and Gianpiero Colonna

Atoms 2022, 10(1), 2; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms10010002 - 22 Dec 2021

Cited by 3 | Viewed by 2200

Abstract

The Binary-Encounter Bethe approach was applied to the estimation of total ionization induced by electron impact in metastable states of diatomic molecules. The cross sections recently obtained for N

_{2}

and CO are reviewed and the new results for H

_{2}

are presented, [...] Read more.

The Binary-Encounter Bethe approach was applied to the estimation of total ionization induced by electron impact in metastable states of diatomic molecules. The cross sections recently obtained for N

_{2}

and CO are reviewed and the new results for H

_{2}

are presented, discussing their reliability through the comparison with other theoretical methods. Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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9 pages, 326 KiB

Open AccessArticle

Binary-Encounter Model for Direct Ionization of Molecules by Positron-Impact

by Małgorzata Franz, Katarzyna Wiciak-Pawłowska and Jan Franz

Atoms 2021, 9(4), 99; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms9040099 - 24 Nov 2021

Cited by 4 | Viewed by 1984

Abstract

We introduce two models for the computation of direct ionization cross sections by positron impact over a wide range of collision energies. The models are based on the binary-encounter-Bethe model and take into account an extension of the Wannier theory. The cross sections computed with these models show good agreement with experimental data. The extensions improve the agreement between theory and experiment for collision energies between the first ionization threshold and the peak of the cross section. The models are based on a small set of parameters, which can be computed with standard quantum chemistry program packages. Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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21 pages, 824 KiB

Open AccessArticle

Population Kinetics Modeling of Low-Temperature Argon Plasma

by Hyun-Kyung Chung, Mi-Young Song, Ji-Won Kwon, Myeong-Geon Lee, Jihoon Park, Namjae Bae, Jeamin Song, Gon-Ho Kim, Dipti and Yuri Ralchenko

Atoms 2021, 9(4), 100; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms9040100 - 24 Nov 2021

Cited by 3 | Viewed by 2303

Abstract

Optical emission spectroscopy has been widely used in low-temperature argon plasma diagnostics. A coronal model is usually used to analyze the measured line ratios for diagnostics with a single temperature and density. However, many plasma processing conditions deviate from single temperature and density, optically thin conditions, or even coronal plasma conditions due to cascades from high-lying states. In this paper, we present a collisional-radiative model to investigate the validity of coronal approximations over a range of plasma conditions of T

_{e}

= 1–4 eV and N

_{e}

= 10

^{8}

–10

^{13}

^{- 3}

. The commonly used line ratios are found to change from a coronal limit where they are independent of N

_{e}

to a collisional-radiative regime where they are not. The effects of multiple-temperature plasma, radiation trapping, wall neutralization, and quenching on the line ratios are investigated to identify the plasma conditions under which these effects are significant. This study demonstrates the importance of the completeness of atomic datasets in applying a collisional-radiative model to low-temperature plasma diagnostics. Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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14 pages, 3598 KiB

Open AccessEditor’s ChoiceArticle

Evaluation of Recommended Cross Sections for the Simulation of Electron Tracks in Water

by Adrián García-Abenza, Ana I. Lozano, Juan C. Oller, Francisco Blanco, Jimena D. Gorfinkiel, Paulo Limão-Vieira and Gustavo García

Atoms 2021, 9(4), 98; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms9040098 - 22 Nov 2021

Cited by 9 | Viewed by 2262

Abstract

The accuracy of the most recent recommended cross sections dataset for electron scattering from gaseous H₂O (J. Phys. Chem. Ref. Data 2021, 50, 023103) is probed in a joint experimental and computational study. Simulations of the magnetically confined electron transport through a gas cell containing H₂O for different beam energies (3, 10 and 70 eV) and pressures (2.5 to 20.0 mTorr) have been performed by using a specifically designed Monte Carlo code. The simulated results have been compared with the corresponding experimental data as well as with simulations performed with Geant4DNA. The comparison made between the experiment and simulation provides insight into possible improvement of the recommended dataset. Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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14 pages, 1900 KiB

Open AccessArticle

Total Cross Sections for Electron and Positron Scattering on Molecules: In Search of the Dispersion Relation

by Fabio Carelli, Kamil Fedus and Grzegorz Karwasz

Atoms 2021, 9(4), 97; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms9040097 - 22 Nov 2021

Cited by 3 | Viewed by 2162

Abstract

More than one hundred years of experimental and theoretical investigations of electron scattering in gases delivered cross-sections in a wide energy range, from few meV to keV. An analogy in optics, characterizing different materials, comes under the name of the dispersion relation, i.e., of the dependence of the refraction index on the light wavelength. The dispersion relation for electron (and positron) scattering was hypothesized in the 1970s, but without clear results. Here, we review experimental, theoretical, and semi-empirical cross-sections for N

_{2}

, CO

_{2}

, CH

_{4}

, and CF

_{4}

in search of any hint for such a relation—unfortunately, without satisfactory conclusions. Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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20 pages, 6910 KiB

Open AccessArticle

Elastic Scattering of Slow Electrons by Noble Gases—The Effective Range Theory and the Rigid Sphere Model

by Kamil Fedus

Atoms 2021, 9(4), 91; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms9040091 - 29 Oct 2021

Cited by 2 | Viewed by 2300

Abstract

We report on an extensive semi-empirical analysis of scattering cross-sections for electron elastic collision with noble gases via the Markov Chain Monte Carlo-Modified Effective Range Theory (MCMC−MERT). In this approach, the contribution of the long-range polarization potential (∼

r^{- 4}

) to [...] Read more.

r^{- 4}

) to the scattering phase shifts is precisely expressed, while the effect of the complex short-range interaction is modeled by simple quadratic expression (the so-called effective range expansion with several adjustable parameters). Additionally, we test a simple potential model of a rigid sphere combined with

r^{- 4}

interaction. Both models, the MERT and the rigid sphere are based on the analytical properties of Mathieu functions, i.e., the solutions of radial Schrödinger equation with pure polarization potential. However, in contrast to MERT, the rigid sphere model depends entirely upon one adjustable parameter—the radius of a hard-core. The model’s validity is assessed by a comparative study against numerous experimental cross-sections and theoretical phase shifts. We show that this simple approach can successfully describe the electron elastic collisions with helium and neon for energies below 1 eV. The purpose of the present analysis is to give insight into the relations between the parameters of both models (that translate into the cross-sections in the very low energy range) and some “macroscopic” features of atoms such as the polarizability and atomic “radii”. Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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9 pages, 7318 KiB

Open AccessArticle

Analytical Cross Section Approximation for Electron Impact Ionization of Alkali and Other Metals, Inert Gases and Hydrogen Atoms

by Rusudan I. Golyatina and Sergey A. Maiorov

Atoms 2021, 9(4), 90; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms9040090 - 27 Oct 2021

Cited by 4 | Viewed by 2343

Abstract

The paper presents an analysis of data on the cross sections of electron impact ionization of atoms of alkali metals, hydrogen, noble gases, some transition metals and Al, Fe, Ni, W, Au, Hg, U. For the selected sets of experimental and theoretical data, an optimal analytical formula is found and approximation coefficients are calculated. The obtained semi-empirical formula reproduces the values of the ionization cross sections in a wide range of energies with an accuracy of the order of error of the available theoretical and experimental data. Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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10 pages, 471 KiB

Open AccessEditor’s ChoiceArticle

Targeted Cross-Section Calculations for Plasma Simulations

by Sebastian Mohr, Maria Tudorovskaya, Martin Hanicinec and Jonathan Tennyson

Atoms 2021, 9(4), 85; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms9040085 - 21 Oct 2021

Cited by 6 | Viewed by 1926

Abstract

Gathering data on electron collisions in plasmas is a vital part of conducting plasma simulations. However, data on neutral radicals and neutrals formed in the plasma by reactions between different radicals are usually not readily available. While these cross-sections can be calculated numerically, this is a time-consuming process and it is not clear from the outset which additional cross-sections are needed for a given plasma process. Hence, identifying species for which additional cross-sections are needed in advance is highly advantageous. Here, we present a structured approach to do this. In this, a chemistry set using estimated data for unknown electron collisions is run in a global plasma model. The results are used to rank the species with regard to their influence on densities of important species such as electrons or neutrals inducing desired surface processes. For this, an algorithm based on graph theory is used. The species ranking helps to make an informed decision on which cross-sections need to be calculated to improve the chemistry set and which can be neglected to save time. The validity of this approach is demonstrated through an example in an SF

_{6}

_{2}

plasma. Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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23 pages, 910 KiB

Open AccessArticle

Electron Impact Excitation of Extreme Ultra-Violet Transitions in Xe⁷–Xe¹⁰ Ions

by Aloka Kumar Sahoo and Lalita Sharma

Atoms 2021, 9(4), 76; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms9040076 - 06 Oct 2021

Cited by 4 | Viewed by 1755

Abstract

In the present work, a detailed study on the electron impact excitation of Xe

^{7 +}

, Xe

^{8 +}

, Xe

^{9 +}

and Xe

^{10 +}

ions for the dipole allowed (E1) transitions in the EUV range of 8–19 nm is [...] Read more.

In the present work, a detailed study on the electron impact excitation of Xe

^{7 +}

, Xe

^{8 +}

, Xe

^{9 +}

and Xe

^{10 +}

ions for the dipole allowed (E1) transitions in the EUV range of 8–19 nm is presented. The multi-configuration Dirac–Fock method is used for the atomic structure calculation including the Breit and QED corrections along with the relativistic configuration interaction approach. We have compared our calculated energy levels, wavelengths and transition rates with other reported experimental and theoretical results. Further, the relativistic distorted wave method is used to calculate the cross sections from the excitation threshold to 3000 eV electron energy. For plasma physics applications, we have reported the fitting parameters of these cross sections using two different formulae for low and high energy ranges. The rate coefficients are also obtained using our calculated cross sections and considering the Maxwellian electron energy distribution function in the electron temperature range from 5 eV to 100 eV. Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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15 pages, 2859 KiB

Open AccessArticle

Electron Ionization of Size-Selected Positively and Negatively Charged Helium Droplets

by Felix Laimer, Fabio Zappa, Elisabeth Gruber and Paul Scheier

Atoms 2021, 9(4), 74; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms9040074 - 05 Oct 2021

Cited by 3 | Viewed by 1468

Abstract

A beam of size-selected charged helium droplets was crossed with an electron beam, and the ion efficiency curves for the product droplets in all different charge states were recorded. We estimate that the selected helium droplets on their passage through the electron beam are hit by several hundred electrons which can interact with the individual He atoms of the droplets. Reaction channels corresponding to the removal or capture of up to eight electrons were identified, and in all cases, inelastic scattering and the formation of metastable helium played a significant role. Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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9 pages, 2243 KiB

Open AccessArticle

Magnetic Angle Changer for Studies of Electronically Excited Long-Living Atomic States

by Łukasz Kłosowski and Mariusz Piwiński

Atoms 2021, 9(4), 71; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms9040071 - 28 Sep 2021

Cited by 2 | Viewed by 1262

Abstract

A new geometry of a magnetic angle changer (MAC) device is proposed, which allows experiments to be run on electron impact excitation of long-lived states of target atoms. The details of the device’s design are presented and discussed together with a numerical analysis [...] Read more.

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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11 pages, 365 KiB

Open AccessArticle

Vibrational Excitation Cross-Section by Positron Impact: A Wave-Packet Dynamics Study

by Luis A. Poveda, Marcio T. do N. Varella and José R. Mohallem

Atoms 2021, 9(3), 64; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms9030064 - 09 Sep 2021

Cited by 4 | Viewed by 1383

Abstract

The vibrational excitation cross-section of a diatomic molecule by positron impact is obtained using wave-packet propagation techniques. The dynamics study was carried on a two-dimensional potential energy surface, which couples a hydrogenlike harmonic oscillator to a positron via a spherically symmetric correlation polarization potential. The cross-section for the excitation of the first vibrational mode is in good agreement with previous reports. Our model suggests that a positron couples to the target vibration by responding instantly to an interaction potential, which depends on the target vibrational coordinate. Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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11 pages, 2406 KiB

Open AccessEditor’s ChoiceArticle

Cross Sections and Rate Coefficients for Vibrational Excitation of H₂O by Electron Impact

by Mehdi Ayouz, Alexandre Faure, Jonathan Tennyson, Maria Tudorovskaya and Viatcheslav Kokoouline

Atoms 2021, 9(3), 62; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms9030062 - 06 Sep 2021

Cited by 7 | Viewed by 2134

Abstract

Cross-sections and thermally averaged rate coefficients for vibration (de-)excitation of a water molecule by electron impact are computed; one and two quanta excitations are considered for all three normal modes. The calculations use a theoretical approach that combines the normal mode approximation for vibrational states of water, a vibrational frame transformation employed to evaluate the scattering matrix for vibrational transitions and the UK molecular R-matrix code. The interval of applicability of the rate coefficients is from 10 to 10,000 K. A comprehensive set of calculations is performed to assess uncertainty of the obtained data. The results should help in modelling non-LTE spectra of water in various astrophysical environments. Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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47 pages, 4057 KiB

Open AccessArticle

Relativistic Study on the Scattering of e^± from Atoms and Ions of the Rn Isonuclear Series

by Mahmudul H. Khandker, A. K. Fazlul Haque, M. M. Haque, M. Masum Billah, Hiroshi Watabe and M. Alfaz Uddin

Atoms 2021, 9(3), 59; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms9030059 - 27 Aug 2021

Cited by 8 | Viewed by 1983

Abstract

Calculations are presented for differential, integrated elastic, momentum transfer, viscosity, inelastic, total cross sections and spin polarization parameters S, T and U for electrons and positrons scattering from atoms and ions of radon isonuclear series in the energy range from 1 eV–1 MeV. In addition, we analyze systematically the details of the critical minima in the elastic differential cross sections along with the positions of the corresponding maximum polarization points in the Sherman function for the aforesaid scattering systems. Coulomb glory is investigated across the ionic series. A short range complex optical potential, comprising static, polarization and exchange (for electron projectile) potentials, is used to describe the scattering from neutral atom. This potential is supplemented by the Coulomb potential for the same purpose for a charged atom. The Dirac partial wave analysis, employing the aforesaid potential, is carried out to calculate the aforesaid scattering observables. A comparison of our results with other theoretical findings shows a reasonable agreement over the studied energy range. Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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19 pages, 3238 KiB

Open AccessEditor’s ChoiceArticle

Accurate Electron Drift Mobility Measurements in Moderately Dense Helium Gas at Several Temperatures

by Armando Francesco Borghesani

Atoms 2021, 9(3), 52; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms9030052 - 04 Aug 2021

Cited by 8 | Viewed by 2003

Abstract

We report new accurate measurements of the drift mobility

μ

of quasifree electrons in moderately dense helium gas in the temperature range

26 K \leq T \leq 300 K

for densities lower than those at which states of electrons localized in bubbles appear. [...] Read more.

We report new accurate measurements of the drift mobility

μ

of quasifree electrons in moderately dense helium gas in the temperature range

26 K \leq T \leq 300 K

for densities lower than those at which states of electrons localized in bubbles appear. By heuristically including multiple-scattering effects into classical kinetic formulas, as previously done for neon and argon, an excellent description of the field E, density N, and temperature T dependence of

μ

is obtained. Moreover, the experimental evidence suggests that the strong decrease of the zero-field density-normalized mobility

μ_{0} N

with increasing N from the low up to intermediate density regime is mainly due to weak localization of electrons caused by the intrinsic disorder of the system, whereas the further decrease of

μ_{0} N

for even larger N is due to electron self-trapping in cavities. We suggest that a distinction between weakly localized and electron bubble states can be done by inspecting the behavior of

μ_{0} N

as a function of N at intermediate densities. Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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11 pages, 3122 KiB

Open AccessArticle

On the Electron Impact Integral Cross-Sections for Butanol and Pentanol Isomers

by Nafees Uddin, Paresh Modak and Bobby Antony

Atoms 2021, 9(3), 43; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms9030043 - 13 Jul 2021

Cited by 3 | Viewed by 2186

Abstract

The need for a reliable and comprehensive database of cross-sections for many atomic and molecular species is immense due to its key role in R&D domains such as plasma modelling, bio-chemical processes, medicine and many other natural and technological environments. Elastic, momentum transfer and total cross-sections of butanol and pentanol isomers by the impact of 6–5000 eV electrons are presented in this work. The calculations were performed by employing the spherical complex optical potential formalism along with single-centre expansion and group additivity rule. The investigations into the presence of isomeric variations reveal that they are more pronounced at low and intermediate energies. Elastic, total cross-sections (with the exception of n-pentanol) and momentum transfer cross-sections for all pentanol isomers are reported here for the first time, to the best of our knowledge. Our momentum transfer cross-sections for butanol isomers are in very good agreement with the experimental and theoretical values available, and in reasonable consensus for other cross-sections. Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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13 pages, 2159 KiB

Open AccessEditor’s ChoiceArticle

Few Body Effects in the Electron and Positron Impact Ionization of Atoms

by R.I. Campeanu and Colm T. Whelan

Atoms 2021, 9(2), 33; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms9020033 - 09 Jun 2021

Cited by 5 | Viewed by 2249

Abstract

Triple differential cross sections (TDCS) are presented for the electron and positron impact ionization of inert gas atoms in a range of energy sharing geometries where a number of significant few body effects compete to define the shape of the TDCS. Using both positrons and electrons as projectiles has opened up the possibility of performing complementary studies which could effectively isolate competing interactions that cannot be separately detected in an experiment with a single projectile. Results will be presented in kinematics where the electron impact ionization appears to be well understood and using the same kinematics positron cross sections will be presented. The kinematics are then varied in order to focus on the role of distortion, post collision interaction (pci), and interference effects. Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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Review

Jump to: Editorial, Research

12 pages, 1593 KiB

Open AccessEditor’s ChoiceReview

A Missing Puzzle in Dissociative Electron Attachment to Biomolecules: The Detection of Radicals

by Sylwia Ptasinska

Atoms 2021, 9(4), 77; https://0-doi-org.brum.beds.ac.uk/10.3390/atoms9040077 - 07 Oct 2021

Cited by 10 | Viewed by 2548

Abstract

Ionizing radiation releases a flood of low-energy electrons that often causes the fragmentation of the molecular species it encounters. Special attention has been paid to the electrons’ contribution to DNA damage via the dissociative electron attachment (DEA) process. Although numerous research groups worldwide have probed these processes in the past, and many significant achievements have been made, some technical challenges have hindered researchers from obtaining a complete picture of DEA. Therefore, this research perspective calls urgently for the implementation of advanced techniques to identify non-charged radicals that form from such a decomposition of gas-phase molecules. Having well-described DEA products offers a promise to benefit society by straddling the boundary between physics, chemistry, and biology, and it brings the tools of atomic and molecular physics to bear on relevant issues of radiation research and medicine. Full article

(This article belongs to the Special Issue Electron Scattering in Gases –from Cross Sections to Plasma Modeling)

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