Direct Ionization Cross Sections Research Articles

Electron impact ionization cross sections of several ionization stages of Kr, Ar and Fe

Direct electron impact ionization cross sections for all ionization stages of Kr were calculated with the modified relativistic binary encounter Bethe model (MRBEB), and excitation–autoionization cross sections were evaluated using the first order many body theory (FOMBT) for Kr+, Kr5+, Kr6+, Kr10+, Kr15+ and Kr17+. Our results were compared to configuration-averaged distorted-wave (CADW) calculations, the widely used Lotz formula, and available experimental results. Comparison between direct ionization cross sections for the Ar and Fe isonuclear series was also done with the goal of assessing the versatility of the MRBEB model.

Positronium formation in the noble gases

We present results based upon our ab initio relativistic optical potential method for the simulation of positronium formation in the noble gases neon, argon, krypton and xenon. The method used in this simulation is based upon an approach, first suggested by Reid and Wadehra, whereby the ionization threshold of the atom is effectively reduced by 6.8 eV, the binding energy of positronium in its ground state. This procedure is then modified in order to account for the fact that positronium formation cross sections tend to zero much more rapidly than the corresponding direct ionization cross sections as the energy of the incident positron increases. The agreement of our positronium formation cross sections with experiment is quite good for argon, krypton and xenon over most of the energy region while for neon our cross sections are generally too small at all energies. Nonetheless, our method predicts positronium formation cross sections in better agreement with experiment than the much more sophisticated theoretical approaches used in the past. We also show that adding positronium formation in this way improves agreement with the measured elastic differential cross section at small scattering angles.

Total, elastic, and inelastic cross sections for positron and electron collisions with tetrahydrofuran

We present total, elastic, and inelastic cross sections for positron and electron scattering from tetrahydrofuran (THF) in the energy range between 1 and 5000 eV. Total cross sections (TCS), positronium formation cross sections, the summed inelastic integral cross sections (ICS) for electronic excitations and direct ionization, as well as elastic differential cross sections (DCS) at selected incident energies, have been measured for positron collisions with THF. The positron beam used to carry out these experiments had an energy resolution in the range 40-100 meV (full-width at half-maximum). We also present TCS results for positron and electron scattering from THF computed within the independent atom model using the screening corrected additivity rule approach. In addition, we calculated positron-impact elastic DCS and the sum over all inelastic ICS (except rotations and vibrations). While our integral and differential positron cross sections are the first of their kind, we compare our TCS with previous literature values for this species. We also provide a comparison between positron and electron-impact cross sections, in order to uncover any differences or similarities in the scattering dynamics with these two different projectiles.

Two-center convergent-close-coupling calculations of positron scattering on magnesium

The two-center convergent-close-coupling method is extended to the calculation of positron scattering from atoms with two valence electrons above an inert ion core. Calculations of positron scattering on magnesium have been performed over a wide energy range. Elastic scattering, Positronium formation, target excitation, and direct ionization cross sections have been calculated. Results are in reasonably good agreement with the experimental data where available. Current results confirm the existence of a low-energy shape resonance predicted by variational and single-center convergent-close-coupling methods.

STORAGE RING CROSS-SECTION MEASUREMENTS FOR ELECTRON IMPACT SINGLE AND DOUBLE IONIZATION OF Fe9 +AND SINGLE IONIZATION OF Fe10 +

We have measured electron impact ionization from the ground state of Fe9 + and Fe10 + over the relative electron–ion collision energy ranges 200–1900 eV and 250–1800 eV, respectively. The ions were confined in an ion storage ring long enough for essentially all metastable levels to radiatively relax to the ground state. For single ionization, we find a number of discrepancies between the existing theoretical cross sections and our results. The calculations appear to neglect some excitation-autoionization (EA) channels, particularly from n = 3 to n' excitations, which are important near threshold, and those from n = 2 → 3 excitations, which contribute at about 650 eV. Conversely, at higher energies the calculations appear to overestimate the importance of EA channels due to excitation into levels where n ⩾ 4. The resulting experimental rate coefficients agree with the most recent theory for Fe9 + to within 16% and for Fe10 + to within 19% at temperatures where these ions are predicted to form in collisional ionization equilibrium. We have also measured double ionization of Fe9 + forming Fe11 + in the energy range 450–3000 eV and found that although there is an appreciable cross section for direct double ionization, the dominant mechanism appears to be through direct ionization of an inner shell electron producing an excited state that subsequently stabilizes through autoionization.

The 4p6 autoionization cross section of Rb atoms excited by low-energy electron impact

The autoionization cross section of rubidium atoms was obtained by measuring the total normalized intensities of ejected-electron spectra arising from the decay of the 4p5n1l1n2l2 autoionizing levels. The electron impact energy range from the 4p6 excitation threshold at 15.31 up to 50 eV was investigated. The cross section reaches the maximum value of (2.9 ± 0.6) × 10−16 cm2 at 21.8 eV impact energy. The general behaviours of the cross section and the role of particular autoionizing configurations in its formation were considered on the basis of large-scale configuration interaction calculations of energies, cross sections, autoionization probabilities in 5snl(n ⩽ 7; l ⩽ 4) and 4d nl(n ⩽ 5; l ⩽ 2) configurations as well as the measured excitation functions for the lowest levels in 5s2 and 4d5s configurations. The resonance behaviour of the cross section between 15.3 and 18.5 eV impact energy is caused exclusively by the negative-ion resonances present close to the excitation thresholds of the (5s2)2P and (4d5s)4P autoionizing levels. At higher impact energies, the autoionization cross section is composed of contributions from the high-lying quartet and doublet levels in 4d5s, 5p and 5s5p, 5d, 6s, 6p configurations. From the comparison of the present data with available experimental and calculated ionization cross sections, the 5s + 4p6 direct ionization cross section of rubidium atoms was determined with the maximum value of (7.2 ± 2.2) × 10−16 cm2 at 36 eV. It was also found that the 4p6 excitation–autoionization is the dominant indirect ionization process contributing over 30% of the total single ionization of rubidium atoms by electron impact in the 15.3–50 eV energy range.

Electron-impact ionization of C+excited states

Nonperturbative close-coupling and perturbative distorted-wave methods are used to calculate electron-impact ionization cross sections for excited states of C${}^{+}$. Both the time-dependent close-coupling and the time-independent distorted-wave methods are used to calculate direct ionization cross sections for the $1{s}^{2}2{s}^{2}3l$ configurations. An $R$ matrix with pseudostates method is used to calculate total ionization cross sections for the $1{s}^{2}2{s}^{2}3l$ configurations, including both direct and indirect excitation-autoionization contributions. Comparison of the results shows both a substantial reduction of the direct ionization cross sections due to nonperturbative effects and a large contribution to the total ionization cross sections due to indirect contributions coming from $2s\ensuremath{\rightarrow}2p$ excitations. The ionization cross-section results will permit the generation of more accurate generalized collisional-radiative ionization coefficients needed for the modeling of moderately dense carbon plasmas.

Electron-impact excitation of the(2p2)1Dand(2s2p)1Poautoionizing states of helium

An experimental study of the excitation of the ($2{p}^{2}$) ${}^{1}D$ and ($2s2p$) ${}^{1}{P}^{o}$ autoionizing states of helium by 250-eV electron impact is presented. The ejected-electron angular distributions and energy spectra are measured in coincidence with the corresponding scattered electrons for a scattering angle of $\ensuremath{-}{13}^{\ensuremath{\circ}}$ and for a range of ejected-electron angles in both the forward and backward directions. Resonance profiles are analyzed in terms of the Shore-Balashov parametrization to obtain the resonance asymmetry ${A}_{\ensuremath{\mu}}$ and yield ${B}_{\ensuremath{\mu}}$ parameters and the direct ionization cross section $f$. The spectra and their parameters are compared to the previous measurements of Lower and Weigold [J. Phys. B. 23, 2819 (1990)] and McDonald and Crowe [J. Phys. B 26, 2887 (1993)]. Comparison is also made with the recent theoretical triply differential cross-section calculations based on the first and second Born approximations. In general, good qualitative agreement is found between the experimental results. Some differences are found at the forward and backward directions. These differences in the shape and magnitude of the cross sections are attributed to the different incoming electron energies used in the experiments. The second Born approximation with inclusion of the three-body Coulomb interaction in the final state agrees reasonably well with experiments in the binary region. However, the ${}^{1}{P}^{o}$ resonance yield parameter ${B}_{\ensuremath{\mu}}$ is significantly overestimated at the recoil region, giving a relatively large recoil peak, in contradiction to the experiment. There is also a discrepancy between the two theories available for the ${}^{1}D$ resonance yield parameter ${B}_{\ensuremath{\mu}}$ in this region. Remaining discrepancies between theories and experiments are also discussed.

Nonlinear Atomic Response to Intense Ultrashort X Rays

The nonlinear absorption mechanisms of neon atoms to intense, femtosecond kilovolt x rays are investigated. The production of Ne(9+) is observed at x-ray frequencies below the Ne(8+), 1s(2) absorption edge and demonstrates a clear quadratic dependence on fluence. Theoretical analysis shows that the production is a combination of the two-photon ionization of Ne(8+) ground state and a high-order sequential process involving single-photon production and ionization of transient excited states on a time scale faster than the Auger decay. We find that the nonlinear direct two-photon ionization cross section is orders of magnitude higher than expected from previous calculations.

Positron ionization of the noble gases

We apply our relativistic complex optical-potential method to investigate positron ionization of the noble gases: neon, argon, krypton and xenon. We compare our results of integrated cross sections for direct ionization with experimental measurements and other theoretical calculations.

Fragmentation in positronium collisions with atoms

Recent positronium collision experiments are reviewed in which the cross-sections for projectile- and/or target-fragmentation processes are determined. In contrast with theory, the likelihood for the latter process appears to be significant for positronium collisions with Xe at only ~3 eV above threshold. Measurements of the total direct ionization cross-section by positron impact, performed to test the reliability of the experimental apparatus and method, are also presented.

Electron impact ionization of atomic target inner-shells

There is a need for reliable theoretical methods to calculate electron-impact total ionization cross sections for the large number of neutral atoms and ions with open shell structures. These cross sections are used in a wide range of scientific and industrial applications, such as astrophysical plasmas, atmospheric science, X-ray lasers, magnetic fusion, radiation physics, semiconductor fabrication, accelerator physics and tumor therapy physics. The binary-encounter-Bethe (BEB) model [1], using an analytic formula that requires only two atomic constants, the binding energy and kinetic energy of the electrons, generates direct ionization cross sections for any neutral atom (or molecule), which are reliable in intensity (15%) and shape from the ionization threshold to a few keV in the incident energy [3], or to thousands keV if we consider its relativistic version(RBEB) [2]. In this work we present K- and L-shell ionization cross sections calculations for heavy atoms.

Level-resolved distorted-wave cross-sections of electron impact ionization of Ar5+

Electron impact ionization cross sections of Ar5+ were calculated using configuration-average (CADW) and level-resolved (LRDW) distorted-wave methods. Direct ionization cross-sections of 2s, 2p, 3s and 3p subshells were calculated within a CADW approximation. The contributions from the excitation autoionization channels were evaluated assuming single excitations from the 2s, 2p, and 3s subshells and in both CADW and LRDW methods. The radiative stabilization of the excitation autoionization channels were found to reduce the excitation autoionization by a small amount.

Electron-impact double ionization of magnesium

Theory and experiment are compared for the electron-impact double ionization of Mg. Direct ionization cross sections, involving the simultaneous ionization of both 3s electrons, are calculated using a non-perturbative time-dependent close-coupling method. Indirect ionization cross sections, involving the ionization of either a 2p or 2s electron followed by autoionization, are calculated using a perturbative time-independent distorted-wave method. At low energies the direct ionization cross sections are found to be in good agreement with experiments, while at the higher energies the indirect ionization cross sections are also found to be in good agreement with experiments.

Single and double ionization of magnesium by H + and He 2+ impact

Theoretical investigations of H+ and He2+ impact single and double ionization of magnesium atoms have been performed in the binary encounter approximation. Direct double ionization cross sections have been calculated in the modified binary encounter model. Accurate expressions of σ ΔE (cross section for energy transfer ΔE) and Hartree–Fock velocity distributions for the target electrons have been used throughout the calculations. Contributions to double ionization from the Auger effect following a vacancy in the 2p shell have been considered in the present work. Our H+ impact single and double ionization cross sections are in good agreement with experimental observations. The calculated He2+ impact single ionization cross sections show satisfactory agreement with experiment but in the case of double ionization, success is limited in the experimentally investigated region (42.5–438 keV amu−1).

Evaluation of direct ionization cross sections for C60 by electron interaction

Partial ionization cross sections corresponding to the production of cations C60q+(q = 1-3) in the electron impact ionization of C60 have been calculated using a modified Jain-Khare semiempirical formalism. The cross sections calculated in the energy range varying from ionization thresholds to 1000 eV revealed a reasonable good agreement with the available experimental and the theoretical data.

H+ and He 2+ impact single and double ionization of lead

H+ and He2+ impact single and double ionization cross sections of ground state lead atoms have been calculated in the binary encounter approximation. Calculations of direct double ionization cross sections have been performed in the modified double binary encounter model. The accurate expressions of σΔE (cross-section for energy transfer ΔE) and Hartree-Fock velocity distributions for the target electrons have been used throughout the calculations. Contributions to double ionization from Auger effect following ionization of inner shells have been considered in the present work. Our H+ impact single and double ionization cross sections are in good agreement with the experimental observations. In calculations of He2+ impact cross sections, the present theoretical approach shows limited success in the experimentally investigated region (50–350 keV amu-1).

ERCS08: A FORTRAN program equipped with a Windows graphics user interface that calculates ECPSSR cross sections for the removal of atomic electrons

ERCS08 is a program for computing the atomic electron removal cross sections. It is written in FORTRAN in order to make it more portable and easier to customize by a large community of physicists, but it also comes with a separate windows graphics user interface control application ERCS08w that makes it easy to quickly prepare the input file, run the program, as well as view and analyze the output. The calculations are based on the ECPSSR theory for direct (Coulomb) ionization and non-radiative electron capture. With versatility in mind, the program allows for selective inclusion or exclusion of individual contributions to the cross sections from effects such as projectile energy loss, Coulomb deflection of the projectile, perturbation of electron's stationary state (polarization and binding), as well as relativity. This makes it straightforward to assess the importance of each effect in a given collision regime. The control application also makes it easy to setup for calculations in inverse kinematics (i.e. ionization of projectile ions by target atoms or ions). Program summary Program title: ERCS08 Catalogue identifier: AECU_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AECU_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 12 832 No. of bytes in distributed program, including test data, etc.: 318 420 Distribution format: tar.gz Programming language: Once the input file is prepared (using a text editor or ERCS08w), all the calculations are done in FORTRAN using double precision. Computer: see “Operating system” below Operating system: The main program (ERCS08) can run on any computer equipped with a FORTRAN compiler. Its pre-compiled executable file (supplied) runs under DOS or Windows. The supplied graphics user interface control application (ERCS08w) requires a Windows operating system. ERCS08w is designed to be used along with a text editor. Any editor can be used, including the one that comes with the operating system (for example, Edit for DOS or Notepad for Windows). Classification: 16.7, 16.8 Nature of problem: ECPSSR has become a typical tag word for a theory that goes beyond the standard plane wave Born approximation (PWBA) in order to predict the cross sections for direct (Coulomb) ionization of atomic electrons by projectile ions, taking into account the energy loss (E) and Coulomb deflection (C) of the projectile, as well as the perturbed stationary state (PSS) and relativistic nature (R) of the target electron. Its treatment of non-radiative electron capture to the projectile goes beyond the Oppenheimer–Brinkman–Kramers approximation (OBK) to include the effects of C, PSS, and R. PSS is described in terms of increased target electron binding (B) due to the presence of the projectile in the vicinity of the target nucleus, and (for direct ionization only) polarization of the target electron cloud (P) while projectile is outside the electron's shell radius. Several modifications of the theory have been recently suggested or endorsed by one of its authors (Lapicki). These modifications are sometimes explicit in the tag word (for example, eCPSSR, eCUSR, ReCPSShsR, etc.) A cross section for the ionization of a target electron is assumed to equal the sum of the cross sections for direct ionization (DI) and electron capture (EC). Solution method: The calculations are based on the ECPSSR theory for direct (Coulomb) ionization and non-radiative electron capture. With versatility in mind, the program allows for selective inclusion or exclusion of individual contributions to the cross sections from effects such as projectile energy loss, Coulomb deflection of the projectile, perturbation of electron's stationary state (polarization and binding), as well as relativity. This makes it straightforward to assess the importance of each effect in a given collision regime. The control application also makes it easy to setup for calculations in inverse kinematics (i.e. ionization of projectile ions by target atoms or ions). Restrictions: The program is restricted to the ionization of K, L, and M electrons. The theory is non-relativistic, which effectively limits its applicability to projectile energies up to about 50 MeV/amu. However, the theory is extended to apply to relativistic light projectiles. Radiative electron capture is not taken into account, since its contribution is found to be negligible in the collision regimes covered by the ECPSSR theory. Unusual features: Windows graphics user interface along with a FORTRAN code for calculations, selective inclusion or exclusion of specific corrections, inclusion of the extension to relativistic light projectiles, inclusion of non-radiative electron capture. Running time: Running the program using the input data provided with the distribution only takes a few seconds.

Electron-impact ionization of atomic ions in the Na isoelectronic sequence

Electron-impact ionization cross-sections and rate coefficients for the Na-like ions Mg+, Ar7+, Kr25+, Sn39+, Xe43+ and W63+ are presented. The direct ionization cross-sections of 2s, 2p and 3s subshells are calculated within a configuration-average distorted-wave (CADW) method. In addition, excitation–autoionization contributions originating from the inner-shell excitations of the type 2s22p63s→2s22p53snl (n=3–6) and 2s22p63s→2s2p63snl (n=3–6) are calculated using both CADW and level-resolved distorted-wave (LLDW) methods. We include the branching ratios for the radiation damping of the autoionizing configurations and levels. The excitation–autoionization contributions are found to be quite large for the lighter ions. For the heavier ions the radiation damping of the excitation–autoionization contribution is found to be significant. We find that the distorted-wave results are in good agreement with available experimental measurements, which only exist for Mg+, Ar7+ and Xe43+. We also find that the computationally simple configuration-average calculations are in reasonable agreement with the computationally demanding level-resolved calculations for the excitation–autoionization contributions for all the Na-like ions studied. In addition, Maxwellian rate coefficients are produced from our cross-sections and are archived in a format useful for plasma modelers.

Electron-impact ionization ofB+

Electron-impact ionization cross sections are calculated for the ground and metastable states of ${\text{B}}^{+}$. Comparisons between perturbative distorted-wave and nonperturbative close-coupling calculations find reductions in the direct ionization cross sections due to long-range electron correlation effects of approximately 10% for the ground state and approximately 15% for the metastable state. Previous crossed-beams experiments, with a metastable to ground ratio of between 50% and 90%, are found to be in reasonable agreement with metastable state close-coupling results. New crossed-beams experiments, with a metastable to ground ratio of only 9%, are found to be in reasonable agreement with ground state close-coupling results. Combined with previous work on neutral B and ${\text{B}}^{2+}$, the nonperturbative close-coupling calculations provide accurate ionization cross sections for the study of edge plasmas in controlled fusion research.