Electron-impact Single Ionization Research Articles

Electron Impact Single Ionization Cross Sections of Ar+ Ion

Binary encounter approximation has been used for theoretical calculations of electron impact single ionization cross sections of singly ionized Ar atom at ground state in the energy range of 29.1eV to 2495.1 eV/amu. The cross sections for energy transfer given by Vriens’ and quantum mechanical Hartree-Fock velocity distributions for target electron have been used in the calculation. The contributions in total single ionization cross sections from 3p and 3s subshells are observed higher than from 2p, and the contributions from 3p first increases with impact energy and then decreases with increase of impact energy whereas the contribution from 3s decreases with impact energy. About 69% of results have ratio factors ≤ 1.5 and 59% have values 1.25. Major contributions to the total ionization cross sections are from 3p and 3s for direct single ionization.

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}.

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.

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.

Theoretical investigation of electron-impact ionization of W<sup>6+</sup> ion

<sec>Due to its unique characteristics, metal tungsten has been selected as the wall material for the tokamak magnetic confinement fusion device. The wall material directly interacts with the plasma for a long time, thus causing tungsten atoms and ions to be sputtered and ionized into different charge states, which then enter the tokamak device as plasma impurities. To ensure stable plasma combustion conditions, highly complex model is currently being used to evaluate the behavior of tungsten impurities and their influence on the tokamak plasma. This requires various high-precision atomic data for tungsten atoms and different ionized states of tungsten ions. Electron collision ionization, as a fundamental atomic physical process, is widely encountered in laboratory and astrophysical plasma environments. The parameters such as electron collision ionization cross-sections and rate coefficients are crucial for plasma radiation transport simulations and state diagnostics.</sec><sec>Electron-impact single-ionization (EISI) cross sections of the ground state and metastable state for W<sup>6+</sup> ions are calculated by using the level-to-level distorted-wave (LLDW) method. The contributions of direct ionization (DI) cross section and excited autoionization (EA) cross section to the total EISI cross section are primarily considered.</sec><sec>Comparison of our calculation results with the experimental data from Stenke et al. (Stenke M, Aichele K, Harthiramani D, Hofmann G, Steidl M, Volpel R, Salzborn E <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://iopscience.iop.org/article/10.1088/0953-4075/28/13/021">1995 <i>J. Phys. B: At. Mol. Opt. Phys.</i> <b>28</b> 2711</ext-link>) reveals that the EISI cross section considering only the ground state is significantly smaller than the experimental result. Therefore, it is imperative to take into account the contribution from the metastable state. To determine the fraction of ions in long-lived energy levels within the parent ion beam, three models are employed.</sec><sec>Our results, which include the contribution of metastable states, accord well with the experimental results of Stenke et al. Compared with the theoretical calculation result of Pindzola et al. our calculaiton provides a more comprehensive understanding of the electron-impact single-ionization process for W<sup>6+</sup> ions. The comparison is illustrated in the attached figure.</sec>

Electron impact single ionization TDCS of H2O at 81 eV for coplanar asymmetric emission of electrons

We report the results of triple differential cross section (TDCS) for the electron impact single ionization of water molecules at incident electron energy 81 eV for coplanar asymmetric emission of electrons. The TDCS results have been obtained in distorted wave second Born approximation using orientation averaged molecular orbital (OAMO) approximation. The TDCS results have been calculated for the ionization of 1b1 and 3a1 molecular orbital of water molecules for the coplanar asymmetric emission of electrons. The obtained theoretical TDCSs are compared with the available measurements as well as with the first Born results. The second Born results are found to be significant by improving agreement with the measurements particularly in the binary peak region.

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.

Direct double ionization for molecules of H2 and N2 induced by electron-impact

The direct double ionization of H2 and N2 molecules induced by electron-impact are investigated theoretically. Our theoretical calculation combines the binary-encounter-Bethe theory employed for molecular electron-impact single ionization and knock-out mechanism derived from the many-body perturbation theory. The process of electron-impact direct double ionization for molecules in our consideration is treated as the coupling of primary single ionization and knock-out process. The knock-out process is constituted by all the possible secondary single ionization processes. There is a good agreement between our theoretical results and available experimental measurements both for the molecules of H2 and N2. Our approach can obtain the cross section of each ionization channel, which is helpful to understanding for ionization competition mechanism of small homo-nuclear diatomic molecules.

Electron-impact ionization of W9+ and W10+

Electron-impact single-ionization (EISI) cross sections for W q+ (q = 9, 10) ions have been calculated by using the level-to-level distorted-wave (LLDW) method with emphasis on the contribution of metastable states to the total ionization cross sections. Contributions from direct-ionization (DI) and excitation-autoionization (EA) processes are taken into account. The calculated cross sections include the contributions from both the ground configuration and the long-lived metastable states with lifetimes exceeding 10−6 s. Calculated cross sections are in good agreement with experimental measurements when the influence of metastable states on the total ionization cross section are well considered.

Electron-Impact Ionization of the Tungsten Ions: W38+ − W45+

In this manuscript, we present our calculations of detailed electron-impact single ionization cross-sections for tungsten ions, spanning charge states W38+− W45+. The level-to-level distorted-wave method implemented in the flexible atomic code (FAC) was used for calculation. Comparison between the present level-to-level distorted wave treatment and previous configuration-averaged calculations has been performed for the W45+ ion, and we explore the possible reason for the difference observed between two calculations. We demonstrate the importance of radiative damping on the total electron-impact ionization cross-section for the W43+ ion. Present calculations provide missing cross-sections for W38+− W45+. The data obtained are expected to be useful for modeling plasmas for fusion applications, especially for the ITER community.

Contribution of the metastable states to electron-impact single ionization for W7+

In this paper, we present the electron-impact single ionization cross sections for W7+. The level-to-level distorted-wave method implemented in the flexible atomic code (FAC) was used for calculation. Contributions from direct ionization (DI) and excitation-autoionization (EA) processes are taken into account. Comparison between the results of previous experimental measurements and the present calculations show a prominent contribution from metastable states in the W7+ ion. We extended the theoretical analysis including level-to-level calculations from long-lived levels of the [Cd]4f135p6 ground configuration and excited, metastable [Cd]4f145p5, [Cd]4f135p55d and [Cd]4f145p45d configurations. Calculated results are in good agreement with experimental data when, within a statistical model, a 56% fraction of parent ions in the ground configuration is assumed.

Electron-impact single ionization of the nitrogen atom

We study electron-impact single ionization for the nitrogen atom by performing level-to-level calculations. The present study includes direct and indirect processes for all levels of the ground configuration. We explain experimental data using the scaled distorted wave cross-sections. Cross-sections obtained for the highest level of the ground configuration are ~70% larger than the ground one. The contribution of the indirect process is equal to ~5% for the ground level, but this contribution reaches ~30% for the highest level of the ground configuration. Good agreement for the single ionization cross-sections is obtained with values calculated using the B-spline R-matrix with the pseudostates method. We compare our results with data from the standard R-matrix with pseudostates calculations. The cross-sections and Maxwellian rate coefficients are tabulated for the electron-impact collisional ionization and excitation-autoionization processes.

Application of Binary Encounter Approximation and Electron Impact on Ionization of Atoms

Semi-classical binary encounter approximation has been used for theoretical calculations of electron impact single ionization cross sections of Xe and Kr and double ionization of Fe atom at ground state. An accurate expression of cross section for energy transfer ΔE (σΔE) as given by Vriens and quantum mechanical Hartree-Fock velocity distributions for target electron have been used in the calculation. In the case of single ionization of Xe, 71% theoretical results lies within valid range of ratio factor less than 2 and 55% have valueless than 1.5. In the case of Kr, 97% of results have ratio factor less than 2 and 34% of results have ratio factor less than 1.1. Gryzinski and Kune model of charged particle impact double ionization of atoms found suitable for describing double ionization of atoms and ions. In the case of double ionization of Fe by electron impact 47% of results have ratio factor less than 2 and 18% of results have ratio factor 1.2. At impact 760 eV, 800 eV and 850 eV having ratio factor 1.01, 0.989 and 0.967. Major contribution in double ionization is 60.16% from (4s,3d) and 31% is from (4s,3p).

Electron-impact ionization of Ar2+

We study electron-impact single-ionization cross-sections for all levels of the ground configuration of the Ar2+ ion using the distorted wave approximation. We investigate the influences of the direct ionization and excitation-autoionization processes on the total single-ionization cross sections. We used corrected energies for the levels of the Ar3+ ion so that the ionization threshold corresponds to the value recommended by National Institute of Standards and Technology (NIST). Radiative damping is taken into account for the ionization cross-sections of the indirect process. Excitations from the 3s and 3p subshells are investigated for the indirect process. We demonstrate that the excitations from the outermost 3p subshell of the ground configuration provide an important contribution to the single ionization cross-sections at low energies. Fairly good agreement with measurements is obtained for the ground level of the Ar2+ ion. We show that the direct ionization provides ~70% at peak of the total single-ionization cross-sections.

Electron-impact ionization for the levels of Fe3＋

Electron-impact single ionization is investigated for the levels of the ground 3d5 and long-lived 3d44s configurations of the Fe3＋ ion. In addition, the Maxwellian rate coefficients are tabulated in the study. The difference among the cross sections reaches ∼11% and ∼17% for the levels of the ground and long-lived configurations, respectively. The excitation autoionization (EA) provides the larger variation of the cross sections compared to the direct ionization (DI). It is demonstrated that the EA cross sections for the levels of the ground configuration vary more strongly compared to the values calculated for the excited configuration. On the other hand, the DI cross sections evaluated for the levels of the ground configuration agree within ∼4% while the difference of ∼9% is obtained for the levels of the long-lived configuration.

Calculation of Electron Impact Single Ionization TDCS of Tungsten Atoms at 200, 500 and 1000 eV

We report triple differential cross-sections (TDCSs) for the electron impact single ionization of tungsten atoms for the ionization taking place from the outer sub shells of tungsten atoms, viz. W (6s), W (5d), W (5p) and W (4f). The study of the electron-induced processes such as ionization, excitation, autoionization from tungsten and its charged states is strongly required to diagnose and model the fusion plasma in magnetic devices such as Tokamaks. Particularly, the cross-section data are important to understand the electron spectroscopy involved in the fusion plasma. In the present study, we report TDCS results for the ionization of W atoms at 200, 500 and 1000 eV projectile energy at different values of scattered electron angles. It was observed that the trends of TDCSs for W (5d) are significantly different from the trends of TDCSs for W (6s), W (5p) and W (4f). It was further observed that the TDCS for W atoms has sensitive dependence on value of momentum transfer and projectile energy.

Electron-impact single and double ionization of Fe12+

The cross sections of electron-impact single and double ionization of Fe12+ are investigated using the distorted-wave (DW) method and two-step approximate formula based on the knockout (KO) mechanism. Both direct and indirect processes are studied in single and double electron-impact ionization. The better agreements between our theoretical results and experiment measurements are obtained contrasted to earlier theoretical works. Adequate indirect ionization channels with larger configurations space are used in our calculation, which is significant for understanding of the mechanism of single and double electron-impact ionization for highly charge ion Fe12+.

Electron impact single ionization differential cross sections of W (6s), W (5d), W (5p) and W (4f)

Electron-induced triple differential cross sections (TDCSs) have been obtained for the few outer sub-shells of tungsten atoms, namely W (6s), W (5d), W (5p) and W (4f). Tungsten and related materials have been recommended as the prime candidates for wall materials in fusion plasma devices. The electron-induced cross-section data are strongly required for the diagnostics and modeling of plasma in such devices. We observe that the trends of TDCSs obtained for the ionization of W (5d) sub-shells are very different from the TDCSs of W (6s), W (5p) and W (4f) in terms of binary and recoil peak locations as well as in the change of magnitude of TDCS with an increasing value of momentum transfer which is due to the open d-shell. The angle and energy-resolved cross-section data of tungsten atoms may be of vital importance in order to understand the spectroscopy of W atoms as wall materials as well as an impurity.

Partial ionization cross sections of Silicon by Electron impact Ionization process

Electron-impact single-ionization cross sections of Si by electron impact have been solved theoretically for the full range of kinematics and collision geometries of practical interest by S.P. Khare theoretical model. The corresponding partial and total ionization cross sections have also been derived in the energy range varying from ionization thresholds to 6000 eV. Comparison of the evaluated partial and total ionization cross sections is made with the experimental and theoretical data wherever available. Objective:Our objective is to find the partial and total ionization cross sections Silicon atom and its fragmentation ion at different energy levels and analysis of results with other available data. Method: In this present work we have measured partial ionization cross sections of Silicon atom using semi-empirical formalism of Jain & Khare due to electron impact at incident electron energy from ionization threshold to 6000 eV. Findings: Comparison of the evaluated partial and total ionization cross sections is made with the experimental and theoretical data wherever available. A good agreement is observed when we compared our data for electron impact ionization cross section for Silicon and its fragment ions. Also some disagreement is found between our data and other available data. Our results are higher for Si2+, Si4+, Si5+ and Si6+ fragment ions. For Silicon atom, good agreement between theory and experiment is achieved. Novelty: The total ionization cross-sections by electron impact of atoms are required in the study of plasma diagnostics, astrophysical and fusion applications, radiation physics, mass spectrometry, ionization in gas discharge, modeling of fusion plasmas, modeling of radiation effects for both materials & medical research and astronomy. We have calculated partial and total ionization cross section for higher energy range i.e from threshold to 6000 eV, which have not been done by other researchers. Keywords: Ionization; cross section; electron impact

Electron impact single ionization of hydrogen molecule by twisted electron beam

In this communication, we present the results of the five-fold differential cross-section (5DCS) and triple differential cross-section (TDCS) for the (e, 2e) process on molecular hydrogen (H2) by the plane wave and the twisted electron beam impact. The formalism is developed within the first Born approximation using the plane wave and the twisted wave for the incident electron beam. We describe the plane wave, Heitler–London type wave function, Coulomb wave for the scattered electron, the H2 molecular state, and the ejected electron. We compare the angular profiles of the 5DCS and TDCS for the different values of orbital angular momentum (OAM) number m of the twisted electron beam with that of the plane wave beam. We also present the 5DCS for different molecular orientations and study the effect of m on the 5DCS. We further investigate the influence of the twisted electron beam on the (e,2e) process on the H2 molecule from the perspective of the ‘Young-type’ interference of the scattered waves, emanating from the two atomic centers of the H2 molecule. We also study the TDCS for macroscopic H2 target to explore the effect of opening angle (θ p) of the twisted electron beam on the TDCS. Our results clearly show the effect of the twisted electron’s OAM number (m) and the opening angle (θ p) on the 5DCS and TDCS of the molecular hydrogen.