Electron-impact Cross Sections Research Articles

DeepCSNet: a deep learning method for predicting electron-impact doubly differential ionization cross sections

Abstract Electron-impact ionization cross sections of atoms and molecules are essential for plasma modelling. However, experimentally determining the absolute cross sections is not easy, and ab initio calculations become computationally prohibitive as molecular complexity increases. Existing AI-based prediction methods suffer from limited data availability and poor generalization. To address these issues, we propose DeepCSNet, a deep learning approach designed to predict electron-impact ionization cross sections using limited training data. We present two configurations of DeepCSNet: one tailored for specific molecules and another for various molecules. Both configurations can typically achieve a relative L2 error less than 5%. The present numerical results, focusing on electron-impact doubly differential ionization cross sections, demonstrate DeepCSNet's generalization ability, predicting cross sections across a wide range of energies and incident angles. Additionally, DeepCSNet shows promising results in predicting cross sections for molecules not included in the training set, even large molecules with more than 10 constituent atoms, highlighting its potential for practical applications.

Electron-impact double ionization cross sections and rate coefficients for Be-like ions: B+ to Ne6+

We report a detailed analysis of the electron-impact double ionization process for Be-like ions, spanning charge states from B+ to Ne6+. We considered both direct and indirect double ionization processes. For direct double ionization, we calculated the cross sections by considering three different processes: ionization-ionization (II), excitation-ionization-ionization (EII), and ionization-excitation-ionization (IEI). Our results show excellent agreement between the measured cross sections for Be-like-B and Be-like-O ions. The agreement is slightly weaker for Be-like-Ne ions when we take the potential of ionized ions in the distorted-wave method. For other ions for which experimental data are not available, our calculations should provide the missing data. We have summarized the trends of electron-impact double ionization cross sections with atomic number for isoelectronic sequences. Finally, we have provided the Maxwellian and non-Maxwellian rate coefficients for these Be-like ions. The data obtained should be useful for both equilibrium and non-equilibrium charge-state distributions in astrophysical research.

Electron-impact ionization cross section of fusion-relevant diatomic molecules containing B

Electron-impact ionization cross section of fusion-relevant diatomic molecules containing B

Absolute electron impact ionization cross-sections for CF4: Three dimensional recoil-ion imaging combined with the relative flow technique.

Here we present measurements of dissociative and non-dissociative cross-sections for the electron impact of the CF4 molecule. The present experiments are based on a Recoil Ion Momentum Spectrometer (RIMS), a standard gas mixing setup for CF4, and a reference gas. The measurements were carried out at several electron energies up to 1keV, covering the energy range of previous experiments. We apply the relative flow technique (RFT) to convert the relative cross-sections measured by the RIMS into absolute values. Using the combination of RIMS and RFT, ion collection and calibration errors were minimized. The results were compared with theoretical and experimental studies available in the literature. Previous electron impact experiments present relative cross-sections or use correction terms for the absolute cross-sections due to losses of energetic ions. We elucidate the differences between the new measurement method and the existing ones in the literature and explain why the present method can be considered reliable. Furthermore, we show how reducing correction terms affects the results.

Electron impact ionization in dense plasmas

The distorted-wave with exchange (DWE) method is employed to evaluate electron impact ionization cross sections in dense electron–ion plasmas. Bound and continuum electron wave functions are obtained from a non-relativistic average-atom code. Plots of DWE cross sections are presented for 1s electrons in Li and Be plasmas and 2p electrons in Na and Mg plasmas. For each of these elements, cross sections are evaluated at metallic density in a range of temperatures from 10 to 100 eV and at their respective melting points. Resonances in the cross sections appear near the incident energy threshold at high temperatures. The origin of these resonances is discussed. In general, the distorted wave (DW) method without exchange is found to be a good approximation to the DWE method for electron impact ionization calculations. In the resonance region, however, exchange effects are found to be very important and cannot be neglected.

(Invited) Numerical Simulation of an Atmospheric Pressure Streamer Discharge and Induced Chemical Reactions

Streamer discharges are a type of non-thermal plasma produced by high-voltage electrical discharges, and have great potential as highly reactive chemical reaction fields. This is mainly due to the generation of high energy electrons that produce chemically active species. The applications of non-thermal plasma have attracted considerable interest in a wide range of industries. However, each radical has a different role in the plasma application and their reaction mechanism is also different. It's therefore important to understand exactly when, where and how much of these reactive species are produced in order to improve the treatment efficiency of atmospheric pressure plasma applications. Against this background, the aim of this study is to develop a simulation model capable of accurately predicting the chemical reactions of radicals. With a sufficiently validated simulation model, it would be possible to use such a model to design chemical reaction fields.The model consists of the first-order electrohydrodynamic model for electrons and positive and negative ions within the drift-diffusion approximation. Axis-symmetric coordinates were used to simulate the streamer discharge in air at atmospheric pressure. The electron transport and source parameters were calculated using two-term bltzmann equation and published electron impact cross-sections. The chemical reaction model used in this study includes electron impact collisions (excitation, ionisation, dissociation, recombination, attachment and detachment), ion recombination and the reactions of neutrals. In order to demonstrate the validity of the simulation, the light emission of the discharge is first compared between experiment and simulation. Then the spatial and temporal variations of each radical are simulated and compared with the simulation. In this talk, I will present the process of validation and verification (V&V) of the streamer discharge simulation and then the mechanism of radical production revealed by the simulation.

Calculation of electron-impact ionization of various benzene derivatives

Calculations of the electron-impact ionization cross-section of pyrene, anthracene, benzoyl chloride, benzophenone, and phthalonitrile are reported over a wide energy range. A comparison of theoretical models, viz. spherical complex optical potential (SCOP), pixel counting method (PCM), and the binary encounter Bethe (BEB) model is carried out. SCOP calculations provide the inelastic cross-section, and the ionization cross-section is extracted from it. This result is modified with PCM, a model previously applied to ion collisions which takes geometric screening corrections into account. The BEB model is used as an independent approach to calculate the ionization cross-section. It is demonstrated that all model results are in reasonable agreement with each other. Comparison is also made with other theoretical data where available.

Differential elastic scattering and electron-impact ionization cross sections of nitrous oxide

With the aim of providing datasets for simulations of electron transport processes in the upper atmosphere, we measured singly differential elastic electron scattering and doubly differential electron-impact ionization cross sections of nitrous oxide. These measurements were conducted for primary electron energies between 30 eV and 1 keV in the angular range of 20°–150°. Secondary electron energies spanned from 4 eV to approximately half of the primary electron energy. In addition to the measurements, the differential elastic scattering cross sections of nitrous oxide were calculated using the IAM-SCAR + I model. Furthermore, the singly differential and total ionization cross sections of nitrous oxide were obtained by integrating the doubly differential ionization cross sections over emission angle and over both emission angle and secondary electron energy, respectively. These cross sections were compared to calculations performed using the BEB model and to experimental results of other groups, who determined the total ionization cross sections of nitrous oxide by collecting ions generated during electron impact.Graphical abstract

Comparative experimental and theoretical study on doubly differential electron-impact ionization cross sections of pyrimidine

Comparative experimental and theoretical study on doubly differential electron-impact ionization cross sections of pyrimidine

L- and M-subshell ionization cross-sections of heavy atoms by electron and proton impact

Inner-shell ionization has many applications related to material analysis. However, full theoretical calculations in heavy multielectronic atoms are scarce. In this contribution, we assess proton and electron impact Li and Mi-subshell ionization cross-sections of heavy targets (72≤Z≤83) using two theoretical models. These calculations are based on the Distorted Plane Wave Born Approximation for electron impact and the shellwise local plasma approximation for the proton impact, combined with relativistic calculations of these deep subshells wave functions and binding energies. We analyze the L-shell ionization of W, Au, and Bi and the M-shell of Hf, Ta, W, Re, Os, Pt, Au, Pb, and Bi. Present values are compared with available experimental data from the literature, with disparate agreement. The convergence of proton and electron impact cross-sections at high-impact velocities is also discussed.

Experimental and theoretical total cross sections for single and double ionization of the open-4d-shell ions Xe12+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{12+}$$\\end{document}, Xe13+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{13+}$$\\end{document}, and Xe14+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{14+}$$\\end{document} by electron impact

We present new experimental and theoretical cross sections for electron-impact single ionization of Xe12+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{12+}$$\\end{document} and Xe13+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{13+}$$\\end{document} ions, and double ionization of Xe12+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{12+}$$\\end{document}, Xe13+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{13+}$$\\end{document} and Xe14+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{14+}$$\\end{document} ions for collision energies from the respective ionization thresholds up to 3500 eV. The calculations use the fully relativistic subconfiguration-averaged distorted-wave approach and, partly, the more detailed level-to-level distorted wave method. We find that, unlike in previous work, our theoretical cross sections agree with our experimental ones within the experimental uncertainties, except for the near-threshold double-ionization cross sections. We attribute this remaining discrepancy to the neglect of direct-double ionization in the present theoretical treatment.Graphical abstractExperimental and theoretical cross sections for electron-impact single ionization of Xe12+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{12+}$$\\end{document}.

Investigation of the cross sections for electron collision ionization of complex molecules

AbstractAn accurate and computationally efficient determination of the cross sections for electron collision ionization of molecules has various applications, such as plasma physics and atmospheric science. In the case of large molecules, ab initio calculations are often difficult and time‐consuming. Here, we develop a feed forward neural network to predict the electron impact ionization cross sections of complex molecules. The training (predicting) set in the method consists of a series of theoretical ionization cross sections for small (large) molecules obtained from the combined model, which integrates the Binary‐Encounter‐Bethe and Deutsch‐Märk models. Several complex systems or targets involving electron collision ionization are evaluated, including molecules such as CH, CH, CH, CH, C, CHO, and CHO. The root mean square errors of the trained and predicted cross sections by the neural network (compared to the values from the combined model) are found to be approximately .0086 and .0930 (in 10 cm), respectively, (using the CHO molecule as an example), indicating our results are very high accuracy. The excellent agreement between the predicted values and the actual values indicates that the neural network is a practical and powerful tool for determining the electron collision ionization cross sections of complex molecules and can provide valuable insights into the dynamics process. Apart from its fundamental importance, this study has far‐reaching implications for gas discharge, low‐temperature plasmas, and fusion edge plasmas and so forth.

BEB-based models for ionisation cross sections of electron and positron impact with diatomic molecules

The ionising interactions of high-energy particles with molecules have applications in many areas. Despite this, some areas, including positron scattering, lack experimental data due to difficulties in performing experiments. Here, quick and simple methods for computing direct electron and positron impact ionisation cross sections are presented. These calculations, performed using the open-source software RAPID-CS, can provide a complete data set as a first approximation for when experimental, or more detailed computational work is not available. The cross-sectional data set includes the total, partial/fragment-specific, single-differential, average secondary electron energy and stopping power cross sections. The molecules N2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}, O2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} and CO were chosen to study due to the availability of positron scattering data. An overall good agreement with experimental and other computational results is presented.Graphical abstractDirect electron (left) and positron right) impact partial ionisation cross sections for N2. Total cross section: red, N2+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N^{+}_{2}$$\\end{document} partial cross section: blue, N+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+}$$\\end{document} partial cross section: green.electron: solid lines: BEB, experimental measurements by Lindsay and Mangan [36]:Ürosses, Straub et al. [37]: stars, Opel et al. [39]: squares. Positron: solid lines: BEB0, Dashed lines: BEBA, Marler and Surko [23]: red crosses, Bluhme et al. [24]: stars

Electron impact single ionization cross-section and Maxwellian rate-coefficients of L-shell of tungsten ions W64+-W71+

The cross-sections and Maxwellian rate coefficients of electron impact single ionization is theoretically investigated for tungsten ions (W64+ to W71+) for fine structure levels of configurations containing n = 2 orbitals. To check the accuracy of calculated cross-sections and rate-coefficients, detailed comparison between result from different approximations, binary encounter dipole (BED), distorted wave (DW) and coulomb born exchange (CBE) is presented. The calculations for electron impact ionization cross-sections of ground state are carried out for energy range 20 keV–1000 keV of final electron and Maxwellian rate coefficients for ground state are evaluated at the temperature range 20 keV–300 keV. We have also provided cross-sections at five different energies and rate-coefficients at five different temperatures. The present study of tungsten ions may be useful in fusion plasma modelling and in future comparison.

Electron impact partial ionization cross sections: R-carvone, 2-butanol, imidazole, and 2-nitroimidazole.

We calculate electron impact partial and total ionization cross sections of R-carvone (C10H14O), 2-butanol (C4H10O), imidazole (C3H4N2), and 2-nitroimidazole (C3H3N3O2). We have used the Binary Encounter Bethe (BEB) model to obtain total electron impact ionization cross sections (TICSs). The modified BEB method in combination with mass spectrum data of the molecules is used to calculate the partial ionization cross section (PICS) of the cationic fragments dissociating from the parent molecule. Our PICS data for R-carvone and 2-butanol are in good agreement with the experimental data for all the cation fragments along with the TICS data. For imidazole and 2-nitroimidazole, the estimates of the PICS are reported for the first time in the present study. We have found that both the modified BEB method and the mass spectrum dependence method work effectively to estimate PICS if we have information about the appearance energies and relative abundance data of the target under investigation.

Theoretical analysis of the electronic structure and electron collision ionization process in a strongly coupled semi-classical plasma environment

In this work, we propose a distorted wave method in the relativistic framework to analyze the electron collision ionization process under the influence of strongly coupled semi-classical plasmas. A pseudopotential is used to represent the screened interactions between the core and outer electron, together with solving the Dirac equation to take care of the relativistic effects. This potential characterizes the plasma in terms of the Debye screening length and the de Broglie wavelength, which takes into account both the quantum mechanical effects of diffraction (short distance) and the collective effects (long distance). With this method, the traditional central-field potential is modified, the bound- and continuum-electron wavefunctions and the collision matrix elements are estimated under a relativistic Dirac–Coulomb framework. The strongly coupled semi-classical plasma effects on the energies, transition rates, and the electron impact ionization cross sections are investigated in detail, using the hydrogen atom as an example. Our results agree well with other available theoretical data. The reported results and the computational scheme are not only of interest to the communities such as atomic and plasma physics, but also have implications for many other areas, including astrophysical objects, inertial confinement fusion plasmas, etc.

Theoretical investigations on electron-impact single-ionization cross section of Sn 11+

The total cross-section of electron-impact single ionization for the ground configuration 3d 104s 24p 64d 3 and excited configuration 3d 104s 24p 64d 24f of Sn 11+ is determined from the ionization threshold to 1000 eV. The contributions of direct ionization, excitation auto-ionization, and resonant excitation double auto-ionization to the total electron-impact single ionization cross-section are systematically demonstrated. The cross-section of direct ionization and excited auto-ionization are determined using the level-to-level method, while the cross-section of partially resonant excited double auto-ionization are determined through the configuration averaged method. To obtain convergence, excitation channels with the maximum principal quantum number up to n = 25 are considered. A comparison of the present results with the experimental data [Borovik et al. J. Phys. B 46, 175 201 (2013)] reveal considerably improved agreement when including the resonant excitation double auto-ionization in the calculation.

Lisbon Atomic Database (LISA): a compilation of calculated fundamental atomic parameters

The Lisbon Atomic Database (LISA) has a dedicated mission of compiling and providing a comprehensive collection of atomic parameters for the study of the interaction of X-rays with matter. This encompassing array of parameters spans a broad spectrum, extending from the calculation of electron impact ionization cross sections (EIICS) using the Modified Relativistic Binary Encounter Bethe model (MRBEB) , to pivotal data such as fluorescence and Coster–Kronig yields of atomic subshells, binding energies, and the full suite of radiative and non-radiative atomic transition parameters. Except for the EIICS values, all these parameters are obtained through ab initio calculations. These calculations are carried out using a self-consistent ab initio Multi-Configuration Dirac–Fock approach, supported by a specialized code developed by Desclaux, Indelicato, and others (MCDFGME).Graphical abstract

Ultraviolet H2luminescence in molecular clouds induced by cosmic rays

Context. Galactic cosmic rays (CRs) play a crucial role in ionisation, dissociation, and excitation processes within dense cloud regions where UV radiation is absorbed by dust grains and gas species. CRs regulate the abundance of ions and radicals, leading to the formation of more and more complex molecular species, and determine the charge distribution on dust grains. A quantitative analysis of these effects is essential for understanding the dynamical and chemical evolution of star-forming regions.Aims. The CR-induced photon flux has a significant impact on the evolution of the dense molecular medium in its gas and dust components. This study evaluates the flux of UV photons generated by CRs to calculate the photon-induced dissociation and ionisation rates of a vast number of atomic and molecular species, as well as the integrated UV photon flux.Methods. To achieve these goals, we took advantage of recent developments in the determination of the spectra of secondary electrons, in the calculation of state-resolved excitation cross sections of H2by electron impact, and of photodissociation and photoionisation cross sections.Results. We calculated the H2level population of each rovibrational level of theX, B, C, B′,D, B″,D′, andastates. We then computed the UV photon spectrum of H2in its line and continuum components between 72 and 700 nm, with unprecedented accuracy, as a function of the CR spectrum incident on a molecular cloud, the H2column density, the isomeric H2composition, and the dust properties. The resulting photodissociation and photoionisation rates are, on average, lower than previous determinations by a factor of about 2, with deviations of up to a factor of 5 for the photodissociation of species such as AlH, C2H2, C2H3, C3H3, LiH, N2, NaCl, NaH, O2+, S2, SiH, l-C4, and l-C5H. A special focus is given to the photoionisation rates of H2, HF, and N2, as well as to the photodissociation of H2, which we find to be orders of magnitude higher than previous estimates. We give parameterisations for both the photorates and the integrated UV photon flux as a function of the CR ionisation rate, which implicitly depends on the H2column density, as well as the dust properties.

Recommended electron-impact excitation and ionization cross sections for Be II

An overview of the current status of electron-impact excitation and ionization cross sections for Be II is given and the recommended data sets for use in plasma modeling are presented. Accurate cross sections between the lowest 14 atomic terms of 1s2nl(n≤5) configurations are calculated with the convergent close-coupling (CCC) method and compared with the available experimental and theoretical results. The recommended electron-impact excitation and ionization cross sections are represented by analytical fitting functions that preserve correct asymptotic behavior. Uncertainties in the recommended data sets are determined by assessing the accuracy of the target structures, the convergence in the subsequent collisional calculations, and the fitting method. They are well within 15 % for most of the transitions. The fitting coefficients for 91 excitation cross sections and 14 ionization cross sections are provided for use in plasma modeling simulations.