Electron Impact Single Ionization Cross 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.

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.

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.

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.

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 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.

Electron impact ionization cross sections of the ground and excited levels of Se3+

Electron impact single ionization cross sections are theoretically investigated from the ionization threshold to 1000eV for the levels belonging to the ground and two lowest excited configurations of ([Ni])4s24p, 4s4p2, and 4s24d of Se3+ using a detailed level-to-level distorted-wave formalism. The ionization cross sections of the two levels belonging to the configuration of 4s24p are nearly equivalent and so are 4s24d, whereas large difference is found for the eight levels of 4s4p2. The theoretical results are utilized to analyze and interpret a recent experimental measurement for the single-ionization cross section of Se3+ (Alna’washi et al., 2014). The population distributions existed in this experiment are deduced. Except for the levels of the ground configuration, there exist populations from levels of the excited configuration of 4s24d.

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.

Electron Impact Single Ionization of Kr and Xe

Theoretical studies of electron impact single ionization cross sections of Kr and Xe atoms have been performed in the Binary Encounter Approximation (BEA). Accurate expression of σΔE (cross-section for energy transferΔE) and the Hartree-Fock (HF) velocity distributions for the target electrons have been used throughout the calculations. The present results of single ionization cross sections are in good agreement with the experimental observations.

Electron impact ionization of silicon and germanium atom

Theoretical studies of electron impact single ionization cross sections of Si and Ge atoms have been performed in the binary encounter approximation (BEA) including exchange and interference as given by Vriens and the Hartree-Fock (HF) velocity distributions for the target electrons have been used throughout the calculations. The present results of single ionization cross sections are in good agreement with the experimental observations.

The 5p6 autoionization cross section of cesium atoms: contribution to single ionization by electron impact

The autoionization cross section of cesium atoms in the incident electron energy range from the 5p6 lowest autoionization threshold at 12.3 eV up to 16.6 eV was investigated for the first time. The data were obtained by summarizing the normalized intensities of lines in ejected-electron spectra observed at the ‘magic’ angle of 54.7°. The autoionization cross section possesses a clear resonance character with a maximum value of 4.8 × 10−16 cm2 at 14.7 eV. By analysing the calculated multiconfiguration Dirac–Fock energies, decay channels and excitation cross sections for the lowest autoionizing configurations it was found that the quartet levels 5p55d6s give the bulk of the autoionization cross section and, therefore, of the autoionization contribution to the single ionization cross section of cesium. Both resonance shape and ‘fine’ structure of the autoionization cross section are caused by the presence of strong negative-ion resonances in the excitation of the levels in configurations 5p56s2, 5p55d6s and 5p56s6p. A comparison of the data is made with available experimental and theoretical electron impact single ionization cross sections of cesium atoms.

Electron impact ionization of helium isoelectronic systems

The electron impact single ionization cross sections, on the helium isoelectronic He, Li1+, B3+, C4+, N5+, O6+, Ne8+, Na9+, Ar+16, Fe24+, Mo41+, Ag45+, and U90+ targets, are calculated modifying the simplified Bell (SBELL) model [Eur. Phys. J. D 46, 281 (2008)]. The results of the present analysis are compared with the available experimental and theoretical data. The modified SBELL (MSBELL) model, incorporating the ionic correction factor in it, produces excellent agreement with the experimental data and theoretical calculations for all the two-electron systems, neutral or ions. This model may be a prudent choice in plasma modeling due to its simple inherent structure.

Two-step single-ionization mechanisms

In a recent publication [Phys. Rev. Lett. 92, 233202 (2004)] two different electron impact double ionization (e,3e) mechanisms were identified and the way in which two-electron momentum distributions for atoms and molecules could be obtained by triple coincidence (e,3e) measurements was discussed. The apparatus used detected the two ejected electrons both in and out of the scattering plane at an angle of 45 deg. to the momentum transfer direction in triple coincidence with the scattered electron. Ejected electrons detected out of the scattering plane were shown to be a result of two-step double ionization processes. With the same apparatus we have made double coincidence (e,2e) measurements of electron impact single ionization cross sections for ionization of magnesium 3s (valence) and 2p and 2s (inner) shell electrons at incident energies from 400 to 3000 eV in order to obtain more information about two-step ionization. The experimental results were compared with distorted-wave and plane-wave Born approximations carried out to second order. For the experimental conditions, two-step ionization processes involving one ionizing collision and a second elastic collision with the atomic core are the dominant contribution to the measured cross sections. Calculations are in moderate agreement with the data. The angular distributions ofmore » the ionized electrons in these two-step ionizations reflect the initial momentum distributions of the target electrons, a result that is analogous with the earlier (e,3e) measurements.« less

Strong contributions of indirect processes to the electron-impact ionization cross section of Sc^{+} ions

We present experimental measurements and theoretical calculations for the electron-impact single ionization cross section of ${\mathrm{Sc}}^{+}$ ions covering an energy range from threshold to $1000\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. An electron-ion crossed-beams setup was employed for the measurements of absolute cross sections as well as for a high-resolution energy scan to uncover fine details in the energy dependence of the cross section. Direct ionization is described by configuration-averaged distorted-wave theory and indirect ionization by $R$-matrix theory. Indirect processes contribute to the total ionization cross section by up to $\ensuremath{\sim}40%$. This finding is related to the existence of strong $3p\ensuremath{\rightarrow}3d$ excitation channels in ${\mathrm{Sc}}^{+}(3{p}^{6}3d4s)$. The shape of the related cross-section feature is reminiscent of the very strong $4d\ensuremath{\rightarrow}4f$ excitation, found in the ionization of xenon and its neighboring elements.

Electron impact single ionization of copper

Electron impact single ionization cross sections of copper have been calculated in the binary encounter approximation using accurate expression for σΔE as given by Vriens and Hartree-Fock momentum distribution for the target electron. The BEA calculation based on the usual procedure does not show satisfactory agreement with experiment in this case but a striking modification is found to be successful in explaining the experimental observations. The discrepancy is linked with the ionization of the 3d10 electrons and probably effective single ionization does not take place from 3d shell of copper leading to smaller values of experimental cross sections.

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.

Quantum Mechanical Calculation of Maximum Electron Impact Single Ionization Cross Sections for the Inert Gases and Small Molecules

Quantum mechanical calculations based on a simple concept of electron impact single ionization have been carried out for the inert gases and several molecules in order to determine maximum electron impact ionization cross sections. For molecular targets, cross sections are calculated as a function of the electron−molecule approach geometry and then averaged over all orientations for the total ionization cross section. These have shown promising agreement with experimentally measured cross sections for randomly oriented molecules and also with existing theoretical methods. The effect of a quantum mechanical method and basis set on the calculated cross section has been found to follow systematic trends.

Calculation of Absolute Outer‐Shell Electron Impact Ionization Cross Sections

AbstractThe recently developed semiempirical DM‐approach for the calculation of electron impact single ionization cross sections is applied here to the ionization of the rare gases (Ne, Ar, Kr and Xe) via ejection of an outer s‐shell electron. The results obtained are compared with previous experimental and theoretical s‐shell ionization cross section functions.