Electron-impact Cross Sections Research Articles

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

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.

Electron-impact single ionization for the N[formula omitted] and N[formula omitted] ions

Electron-impact ionization cross sections are investigated for the ground levels of N2+ and N3+ ions. Additionally, the long-lived energy levels of the N2+2s2p2 and N3+2s2p configurations are analyzed. Study includes both direct and indirect ionization processes. Contribution of the excitation–autoionization (EA) channels to the ionization cross sections is approximately 15% to 23% for both ions. Convergence of the EA cross sections is analyzed by considering excitations up to shells with the principal quantum numbers n⩽20. The obtained results are compared to available experimental data for the N2+ and N3+ ions.

Fast computation approach of electron-impact ionization and excitation cross-sections for atoms and ions with medium- and high-<i>Z</i> elements

The atomic data of medium- and high-<i>Z</i> elements, such as electron-impact ionization and excitation cross-sections, possess extensive applications in fields such as fusion science and X-ray interactions with matter. There are atoms and ions in high energy density plasma, with different charge states and energy states ranging from ground states to highly excited states, and the cross-sections of each charge state and energy state need to be calculated. The bottlenecks limiting computational performance are the inevitable relativistic effects of medium- and high-<i>Z</i> elements and the extremely complex electronic configurations. Taking tantalum (Ta) for example, by using the relativistic Dirac-Fock theory and distorted wave model, we compute the electron-impact ionization and excitation cross-sections of Ta from the ground state atom up to Ta<sup>72+</sup> with the incident electron energy range of 1–150 keV. The detailed configuration accounting (DCA) reaction channel cross-sections are derived by summing and weighting the original detailed level accounting (DLA) cross-sections. After examining the data, two regularities are found. In terms of DLA, the pre-averaging DCA cross-sections have varying initial DLA energy levels but are typically close to each other. There is not a straightforward function that can explain the discrepancies between them. In terms of DCA, inner subshells typically contribute very little to the total cross-section as their ionization and excitation cross-sections are orders of magnitude smaller than those of outer subshells. We provide two techniques to reduce the computational costs based on the regularities. To minimize the total number of DLA reaction channels used in the computation, the initial DLA energy levels can be randomly sampled. Through a Monte Carlo numerical experiment, we determine the appropriate number of sampling points that can reduce the total number of DLA channels by an order of magnitude while maintaining a 5% error margin. In terms of impact ionization, since small cross-section DCA channels are insignificant, only a tiny portion of the DCA channels are required to preserve a 95% accuracy of the entire cross-section. It is possible to use the analytical Binary Encounter Bethe (BEB) formula to determine which DCA channels should be neglected before the computation to reduce computational costs. In terms of electron-impact excitation, just the cross-sections of the same excited subshells as the preserved ionized subshells, which are determined in the previous electron-impact ionization (EII) calculations, are needed. Finally, we compare our EII results with theoretical and experimental results. In the low incident electron energy range of below 2 keV, our results accord with the theoretical result of the 6s EII cross-section of the Ta atom and the experimental result of the total EII cross-section of the Ta<sup>1+</sup> ion. In the high energy range of below 150 keV, our results are also consistent with the theoretical result of the 1s EII cross-section of the Ta atom and the experimental result of the 1s EII cross-section of the Cu atom. Our results reasonably match the previous experimental and theoretical results in low-energy range and high-energy range, inner subshell and outer subshell, indicating the accuracy of our calculation. The proposed optimizing strategy can be applied to various medium- to high-<i>Z</i> elements and is compatible to most computation codes.

Theoretical investigation of electron-impact ionization of W8+ ion

The electron-impact single ionization cross section for W8+ ion has been calculated using flexible atomic code, employing the level-to-level distorted-wave approximation. This calculations takes into account contributions form both direct ionization (DI) and excitation autoionization (EA). However, the theoretical predictions, based solely on the ground state, tends to underestimate the experimental values. This discrepancy can be mitigated by incorporation contributions from excited states. We extended the theoretical analysis, including the contributions from the long-lived metastable states with lifetimes exceeding 1.5 × 10−5 s. We employed two statistical models to predict the fraction of ground state ions in the parent ion beam. Assuming a 79% fraction of parent ions in ground configuration, the experiment measurements align with the predictions. Furthermore we derived the theoretical cross-section for the ground state as correlated plasma rate coefficients, and compared it with existing data. Despite the uncertainty in our calculations, our results are still acceptable.

Atomic structure calculations, and electron impact ionization cross-sections of W LXI

The present study provides a wide range of calculations of atomic structure data for the tungsten ion W LXI, that belongs to the silicon isoelectronic sequence. The fully relativistic Multi-configuration Dira-Hartree–Fock (MCDHF) method including configuration interaction (CI) is applied to the current ion. Calculated results of energy levels, oscillator strengths, and radiative rates of W LXI are presented. A set of two configuration state lists including the configurations of 3s23p2, 3s3p3, 3s23p3d, and 3p4 at different angular momenta (J) and parity (P) are considered in the configuration interaction calculations of level energies and oscillator strengths. To increase the accuracy of the results, the electronic correlations from higher orbitals, i.e., 7l orbitals are included in the calculations. Quantum electrodynamics effects such as vacuum polarization and self-energy are recalled in the CI calculations. Many more transitions in the soft x-ray region (between 20 and 200 angstroms) have been identified. The flexible atomic code package has been used to compute the electron impact ionization cross-sections of 3s23p2 3P0,1, 1D2 levels in silicon-like tungsten. The cross-sections of the transitions from the ground level in W LXI to the first levels in the 61st ionization of tungsten have been computed using FAC code. The total ionization cross-sections of the 3s23p2 at electron energy range from 5–35 keV are evaluated as well.

Electron Impact Cross Sections and Transport Studies of C3F6O

Electron Impact Cross Sections and Transport Studies of C3F6O

Electron impact ionization of prebiotic interstellar molecules

This article presents an investigation into the electron impact ionization of diverse prebiotic molecules that exist within the interstellar medium. Specifically, the molecules under consideration here include ethylene glycol, ethanolamine, glycolonitrile, aminoacetonitrile, acetamide, and glycolaldehyde. These molecules hold the potential to serve as precursor compounds, playing a critical role in the formation of essential building blocks necessary for life’s emergence. To understand the chemistry in these regions when such molecules interact with particles like electrons, we require reaction rates and cross sections. In this work, the electron impact ionization cross section is calculated using the robust optical potential approach and the complex scattering potential-ionization cross section method over a wide range of energies from 10 eV to 5000 eV on a fine grid. The incorporation of screening correction in this approach effectively addresses the superimposition of charge densities originating from distinct atoms within each molecule. Additionally, the binary-encounter Bethe ionization cross section is computed to facilitate comparison and validation of the presented data.

On the electron impact cross-section maxima for dissociative and non-dissociative single ionization of molecules and radicals

Determining absolute electron impact ionization cross-sections for atoms and molecules, whether through experimental or theoretical means, poses a formidable challenge and is typically limited to a narrow selection of species. In this paper, by using measured cross-sections and polarizability data, it was obtained empirical scaling laws for total single ionization and non-dissociative single ionization cross-section maximum of neutral molecules by collisions with electrons. It is found that the total single ionization cross-sections scale linearly with the target electric static polarizability, while the non-dissociate cross-sections exhibit a saturation effect for large target polarizabilities. This saturation effect is interpreted as the increasing role of fragmentation with polarizability.

Dehydrogenation in Electron-Induced Dissociative Ionization of Pyridine Molecule

"The electron-impact dissociative ionization of pyridine has been investigated using mass spectrometry. Thirty-two well-resolved mass peaks have been identified in the cation mass spectra and assigned to the most likely ionic molecular fragments. The new sixteen ionic fragments' appearance energies have been determined, and sixteen others remeasured. The total cross-section for electron-impact ionization of pyridine has been measured at 100 eV. Thorough analysis indicates that at least three peaks' groups in the mass spectra occur via the shake-off dehydrogenation mechanism, i.e., by sequential hydrogen atoms elimination from the pyridine parent cation or its fragmentation products. The nature of this process is deciphered. "

Electron impact scattering and electronic excitation in glycolaldehyde: The first ever detected sugar in space

Detailed theoretical investigations on structural, spectroscopic and electron scattering cross sections of glycolaldehyde, the first ever detected sugar in space are reported in this work. Spectroscopic calculations are performed on the ground and excited states of glycolaldehyde using density functional theory (DFT) and time-dependent density functional theory (TDDFT), respectively. The optimized geometrical parameters and vibrational spectrum are in good agreement with the earlier reported work. Vertical excited state (VES) energies at the TDDFT/B3LYP/aug-cc-PVQZ level of theory along with detailed assignments are reported up to 30 transitions. The TDDFT predicted Rydberg series energies are compared with the Rydberg series of glycolaldehyde converging to its first IP, computed using the standard Rydberg formula and are found to be in good agreement. In the absence of sufficient experimental data on excited states of glycolaldehyde, the theoretical results are validated by comparison of VES calculations performed at the same level of theory with the available experimental data for an analogous molecule viz. acetaldehyde. Triplet excited-state energies for glycolaldehyde are reported here for the first time. Electron impact cross section calculations in the energy range 0.1 to 20 eV are carried out using ab-initio R-matrix method. We have detected one π* shape resonance in all the three models viz. SE, SEP and CC, which may also lead to a possible fragmentation channel wherein a hydrogen atom is removed from the molecule forming a glycolaldehyde dehydrogenated anionic radical (C2H3O2−). The π* shape resonance is correlated with the corresponding molecular orbital electronic structure calculations. Additionally, differential, electronic excitation, ionization and total cross sections are reported here for the first time.

Triply differential cross sections for electron and positron impact on methane.

We here report theoretical triply differential cross sections (TDCS) for 250eV electron and positron impact ionization of the methane molecule calculated within the second-order distorted-wave Born approximation (DWBA2) for various momentum transfer conditions. The experimental data taken from Işık et al. [J. Phys. B: At., Mol. Opt. Phys. 49, 065203 (2016)] will be compared with the current theoretical predictions as well as molecular three body distorted wave (M3DW) approximation and generalized Sturmian function (GSF) theoretical models in a non-coplanar geometry. In the low analyzer scattering plane, the results obtained within the DWBA2 theory show better agreement with the experimental results compared to the GSF results. The M3DW results also exhibit agreement with the experimental results, in particular in the perpendicular plane geometry. Furthermore, significant differences between electron and positron TDCS were observed.

Molecular data needs for advanced collisional-radiative modelling for hydrogen plasmas

Population models for molecular hydrogen (H2) are applicable in various fields of plasma physics and particularly in fusion research: they are necessary for the evaluation of plasma diagnostics (e.g. optical emission spectroscopy) or can be used to evaluate effective reaction rates for molecular processes (e.g. molecular-assisted recombination in divertor plasmas). The accuracy and completeness of population models for molecular hydrogen is strongly linked to the accuracy and availability of molecular reaction data. While there are recently huge improvements in the field of electron impact cross sections, the shortfalls regarding input data availability persist in the area of collisions between heavy particles and H2. An overview of the status of population models for H and H2 based on the Yacora solver is given. The data needs for collisional-radiative modelling are demonstrated by means of three examples comprising different detail levels, namely a purely electronic collisional-radiative model for the singlet system of H2, a corona model for the Fulcher-α band and a vibrationally resolved collisional-radiative model for the electronic ground state X1 of H2.Graphical abstractElectronic energy level diagram of the hydrogen molecule delimiting the population models discussed in this work

Electron impact cross-sections and rate coefficients of Si+2 ions relevant to collisional radiative modeling of silicon plasma

We report on the fine structure resolved electron impact excitation (EIE) cross-sections of Si+2 from its ground state 3s 2 (J= 0) to the 41 excited fine structure levels of the configurations 3s3p, 3p 2, 3s3d, 3s4s, 3s4p, 3s5s, 3s4d, 3s4f, 3s5p, 3s5d and 3s5f using relativistic distorted wave theory. The excitation cross-sections from the excited metastable levels (3P0,3P2) of the configuration 3s3p to higher excited levels as well as for some other dominant transitions relevant to plasma modeling are also obtained. In addition, the ionization cross-sections are evaluated from the ground and metastable levels to higher ionized state Si+3 (2S1/2). The calculated cross-sections are utilized to obtain the rate coefficients corresponding to EIE and ionization processes affecting the intensity of prominent Si+2 emission lines 379.61, 380.65, 456.78, and 457.48 nm recorded through optical emission spectroscopic measurements by Wang et al (2020 Phys. Plasmas 27 063513) on laser produced silicon plasma. Further, the rate coefficients corresponding to radiative, and three body recombination are also presented. The reported cross-sections and rate coefficients will be useful for developing rigorous collisional radiative model for the diagnostics of silicon plasma.