Cross Sections For Electron-impact Single Ionization Research Articles

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.

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

Ionization cross-sections of L-shell and L-subshells by electron impact

SynopsisVaisburd and Evdokimov proposed an empirical VE model to calculate the electron impact single ionization cross-sections of atoms and molecules. The extension of the modified VE model (MVE) has been proposed incorporating the relativistic effects. This model is applied to investigate the total L-shell as well as L1-, L2- and L3-subshells ionization cross-sections of various atomic targets with atomic numbers Z =1892 for incident energies up to 1 GeV. The results from the MVE model are compared with the available experimental data and theoretical findings.

Electron-impact ionization ofW5+

Electron-impact single-ionization cross sections for the ${\mathrm{W}}^{5+}$ ion have been studied experimentally and theoretically. Measurements of a detailed ionization spectrum and of absolute cross sections were performed employing the crossed-beams method in the energy range from the ionization onset up to 1000 eV. The experimental data show a prominent contribution of ${\mathrm{W}}^{5+}$ ions in metastable states. The theoretical analysis includes level-to-level calculations from the $4{f}^{14}5{s}^{2}5{p}^{6}5d$ ground configuration and long-lived levels of the $6s$, $5{p}^{5}5{d}^{2}$, $4{f}^{13}5{d}^{2}$, and $4{f}^{13}5d\phantom{\rule{0.16em}{0ex}}6s$ configurations. Direct-ionization and excitation-autoionization contributions to the total single-ionization cross sections were calculated employing a distorted-wave approximation. Radiative damping was taken into account. It is shown that correlation effects play an important role and lead to substantial reduction of cross sections. Theory and experiment are in quite good agreement when, within a statistical model, a ($85\ifmmode\pm\else\textpm\fi{}9$)% fraction of parent ions in the ground configuration is assumed. The strongest contributions of metastable parent ions arise from the $5{p}^{5}5{d}^{2}$ and $4{f}^{13}5{d}^{2}$ configurations.

Electron-impact single ionizaiton for W4+ and W5+**Project supported by the National Natural Science Foundation of China (Grant Nos. 2017YFA0402300, 11464042, 11564036, 11774292, and 11464040) and the Basic Scientific Research Foundation for Institution of Higher Learning of Gansu Province, China.

Electron-impact single ionization cross sections for Wq+ (q = 4–5) were calculated using the flexible atomic code (FAC) in the level-to-level distorted-wave method, considering the explicit branching ratio. The calculated cross sections are compared with the available theoretical and experiment results in detail. In the case of the contribution from the same channles as the available theoretical results, all of the calculated ionization cross sections agree with the experimental measured cross sections. But the present calculated results are larger than the experimental measurement when all channels contributions are included. Some important channels excitation autoionization (EA) contributions, such as the excitation to higher higher subshell from 4f and 5[s,p], were not included into the available theoretical calculation. In general, the distorted-wave (DW) results are overestimated.

Excitation and ionization of outer shells in Rb by electron impact

The relativistic distorted-wave and binary-encounter-dipole approximations were employed for calculating the electron-impact single ionization cross sections of the 5s, 4p6, 4s2, 3d10 shells and 4p6 excitation cross section for Rb atom taking into account both configuration interaction and relativistic effects. The capabilities of the most used theoretical approaches in describing the single ionization of Rb atom were considered by comparing the present and other available calculated data with the experimental total ionization and total direct single ionization cross sections over the electron-impact energy range from the 5s threshold to 600 eV. The best agreement within experimental uncertainty was obtained by using the non-relativistic binary-encounter-dipole approximation included in the LANL Atomic Physics Codes package. At present none of the used approximations (plane-wave Born or relativistic distorted wave) can satisfactorily describe the experimental excitation-autoionization cross section in rubidium because the efficient formation of the 4p6 core-excited negative-ion rubidium states at near-threshold impact energies is ignored in calculations.

Tungsten Ions in Plasmas: Statistical Theory of Radiative-Collisional Processes

The statistical model for calculations of the collisional-radiative processes in plasmas with tungsten impurity was developed. The electron structure of tungsten multielectron ions is considered in terms of both the Thomas-Fermi model and the Brandt-Lundquist model of collective oscillations of atomic electron density. The excitation or ionization of atomic electrons by plasma electron impacts are represented as photo-processes under the action of flux of equivalent photons introduced by E. Fermi. The total electron impact single ionization cross-sections of ions Wk+ with respective rates have been calculated and compared with the available experimental and modeling data (e.g., CADW). Plasma radiative losses on tungsten impurity were also calculated in a wide range of electron temperatures 1 eV–20 keV. The numerical code TFATOM was developed for calculations of radiative-collisional processes involving tungsten ions. The needed computational resources for TFATOM code are orders of magnitudes less than for the other conventional numerical codes. The transition from corona to Boltzmann limit was investigated in detail. The results of statistical approach have been tested by comparison with the vast experimental and conventional code data for a set of ions Wk+. It is shown that the universal statistical model accuracy for the ionization cross-sections and radiation losses is within the data scattering of significantly more complex quantum numerical codes, using different approximations for the calculation of atomic structure and the electronic cross-sections.

Universal statistical approach to radiative and collisional processes with multielectron ions in plasmas

The universal statistical approach for calculation of radiative and collisional processes with multielectron ions in plasmas is developed. It is based on the atomic structure representation similar to that used in a condensed medium. The distribution of local atomic electron density determines the set of elementary excitations with classical plasma frequency. The statistical method is tested by the calculations of the total electron impact single ionization cross-sections, ionization rates and radiative losses of various ions. In the coronal limit the radiative losses of heavy plasma impurities with any type of multielectron ions are determined by the excitation of collective atomic oscillations due to collisions with plasma electrons. It is shown that for low plasma densities the tungsten ions total radiative loss scatter within universal statistical approach does not exceed similar results of current complex numerical codes in the wide range of plasma temperatures. The general expression for the radiative losses in the case of the intermediate state between limiting cases of coronal and Boltzmann population distributions is derived as well. The total electron impact ionization cross-sections and ionization rates for ions of various charge stages for a wide range of elements from Ar to U are compared with experimental and conventional complex code data showing satisfactory agreement. As the universal statistical method operates in terms of collective excitations, it implicitly includes direct and indirect ionization processes.

Detailed investigation of electron-impact single-ionization cross sections and plasma rate coefficients of N-shell tin ions

Electron-impact single-ionization cross sections of Snq + ions in charge states q = 4–13 with 4d[10 − (q − 4)] outer-shell configurations have been studied in the energy range from the corresponding thresholds up to 1000 eV. Absolute cross sections and fine-step energy-scan data have been measured employing the crossed-beams technique. Contributions of different ionization mechanisms have been analysed by comparing the experimental data with calculations employing the configuration-averaged distorted wave approximation. Ionization plasma rate coefficients inferred from the experimental data are also presented.

Electron-impact single-ionization of Ar6+ ions

Electron-impact single-ionization cross sections of Ar6+ ions have been measured in the energy region from below 14 eV up to 1000 eV. Strong contributions of indirect-ionization processes involving excitation of the 2p subshell have been observed. Ions in long-lived excited states were present in the primary ion beam and resulted in ionization onsets below the ground-state ionization threshold.

Electron-impact single-ionization of Ar5+ ions

Electron-impact single-ionization cross sections of Ar5+ ions have been measured employing the crossed-beams technique. In the comparison with former experimental data sets significant discrepancies became apparent. In the energy region from 240 eV up to 300 eV strong contributions from indirect-ionization processes involving excitation of the 2p subshell were observed.

Applicability of Vaisburd and Evdokimov Model to Ionic Targets

The Vaisburd and Evdokimov proposed an empirical model to calculate the electron impact single ionization cross-sections of atoms and molecules. The model has been applied to some atoms and molecules. To examine the efficiency of the model, the present work applies the model to calculate cross-sections for Ne-isonuclear series Ne+, Ne2+, Ne3+, Ne4+, Ne5+, Ne6+, Ne7+, Ne8+, Ne9+ . The separate sets of values of the parameters of the model are determined by comparison with the available experimental data using a non-linear least-squares fitting computer code. Keywords: Electron impact ionization; Empirical model; Ionic targets. © 2012 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi: http://dx.doi.org/10.3329/jsr.v4i2.8704 J. Sci. Res. 4 (2), 307-313 (2012)

Electron impact ionization of beryllium isoelectronic ions

The electron impact single ionization cross-sections on the Be, B +, C 2+, N 3+, O 4+, Ne 6+, Fe 22+ and U 88+ atomic targets, in the beryllium isoelectronic sequence (BIS), are calculated using the modified versions of simplified improved binary-encounter dipole model (siBED) [W.M. Huo, Phys. Rev. A 64 (2001) 042719]. The modified models, QIBED (with the ionic correction) and RQIBED (with both the ionic and relativistic corrections) [M.A. Uddin, A.K.F. Haque, A.K. Basak, B.C. Saha, Phys. Rev. A 70 (2004) 032706], are found to provide an excellent description of the experimental data for all the targets in BIS with the same generic values of the two parameters d 1 and d 2 in the models. The RQIBED results describe satisfactorily the assessed data of Be and its predictions for U 88+ account for well the experimental K-shell ionization data of Sn, with almost the same properties of the ionized orbit concerned, even up to around 2 MeV.

Calculations of electron-impact single-ionization cross sections of helium isoelectronic systems

The electron-impact single-ionization cross sections on the helium isoelectronic targets $\mathrm{He}$, ${\mathrm{Li}}^{+}$, ${\mathrm{B}}^{3+}$, ${\mathrm{C}}^{4+}$, ${\mathrm{N}}^{5+}$, ${\mathrm{O}}^{5+}$, ${\mathrm{Ne}}^{8+}$, ${\mathrm{Na}}^{9+}$, ${\mathrm{Fe}}^{24+}$, ${\mathrm{Ag}}^{45+}$, and ${\mathrm{U}}^{90+}$, are calculated using the recent simplified version of the binary-encounter dipole (siBED) model as applied by Huo [Phys. Rev. A 64, 042719 (2001)] to various molecular targets. The simple siBED model is good for the helium atom, but it is inadequate for ionic targets. Our proposed modifications: (i) ionic correction of the siBED model (QIBED) and (ii) relativistic corrections of the siBED model (RQIBED) are examined on a wider group of species and compared with other available experimental and theoretical results. The predictions of QIBED in the nonrelativistic energy domain and of RQIBED for all energies, with the same parameter values of siBED, produce excellent agreement with the experimental data and the results close to those of other theories for all the two-electron systems, neutral or ions on the same footing.

Electron-impact single ionization of multiplycharged aluminium ions

Absolute total cross sections for electron-impact singleionization of Alq + (q = 3-7) ions areinvestigated experimentally as well as theoretically.Employing the crossed-beams technique, the cross sectionshave been measured from below the respective ground statethreshold up to 1 keV and partly up to 5.5 keV. Thetheoretical calculations were performed using theconfiguration-averaged {distorted-wave} method,including both direct ionization andexcitation-autoionization contributions from the 2p-shell. The measurements are in good agreement withthe calculations considering a small content ofmetastable ions in the incident ion beam. Because of thestrong dominance by direct ionization processes thesemiempirical Lotz formula can describe the measured dataas well.

Theoretical determination of the absolute electron impact ionization cross-section function for silver clusters Agn (n=2–7)

A recently developed semiclassical approach (DM formalism) was used to calculate the absolute total electron-impact single ionization cross sections for silver clusters Agn (n=2–7) from threshold to 1000 eV. Similar to other cluster properties, a clear odd–even effect has been observed for the calculated cross sections and is ascribed to the effective electron numbers in the valence shell. The only available experimental data for comparison are partial cross sections for the production of the singly charged parent ions for the monomer up to the tetramer. No experimental data are available as yet for any larger clusters nor for the total ionization cross sections. Nevertheless, a comparison of the results of the present calculations with calculations using additivity rules applied to molecules and clusters gives valuable insight into the ionization behavior of clusters as a function of cluster size and thus elucidates the transition from a molecular-type situation where the cross sections of the constituents are additive to a cluster-type situation where geometric effects lead to a n2/3-dependence in the limit of large cluster sizes n.

Electron impact single and double ionization of halogens

The binary encounter approximation has been used for calculations of electron impact single ionization cross-sections for F, Cl, Br and I and double ionization cross-sections for Br and I. Contributions of ionization from inner shells have also been included in the calculations. Hartree-Fock momentum distribution has been used for the bound electron as far as possible. The results have been found to be in satisfactory agreement with experimental observations.