Electron-impact Multiple Ionization Research Articles

Theoretical investigation of electron-impact multiple ionization of O ii-iv ions

The electron-impact double ionization (DI) and triple ionization (TI) for O ii-iv ions are investigated using multistep approaches within the framework of many-body perturbation theory. The indirect DI and TI are treated as the single ionization of an inner-shell $1s$ electron followed by the single and double Auger decays, respectively. The knockout mechanism is employed to deal with the direct ionization process. The present approaches reproduce the available experimental cross sections for the DI of O ii-iv ions with much better accuracy compared to previous calculations. The TI cross sections of the O ii ion are calculated, which are in good agreement with the recent experimental data [Lecointre et al., J. Phys. B 46, 205201 (2013)]. It is found that the electron correlation effect and the energy distribution of the intermediate electron, which is taken as the incident electron of the subsequent knockout process, play an important role in the multistep treatment of the multiple ionization process.

Electron-impact Multiple-ionization Cross Sections for Atoms and Ions of Helium through Zinc

Abstract We compiled a set of electron-impact multiple-ionization (EIMI) cross section for astrophysically relevant ions. EIMIs can have a significant effect on the ionization balance of non-equilibrium plasmas. For example, it can be important if there is a rapid change in the electron temperature or if there is a non-thermal electron energy distribution, such as a kappa distribution. Cross section for EIMI are needed in order to account for these processes in plasma modeling and for spectroscopic interpretation. Here, we describe our comparison of proposed semiempirical formulae to available experimental EIMI cross-section data. Based on this comparison, we interpolated and extrapolated fitting parameters to systems that have not yet been measured. A tabulation of the fit parameters is provided for 3466 EIMI cross sections and the associated Maxwellian plasma rate coefficients. We also highlight some outstanding issues that remain to be resolved.

A SIMPLE METHOD FOR MODELING COLLISION PROCESSES IN PLASMAS WITH A KAPPA ENERGY DISTRIBUTION

We demonstrate that a nonthermal distribution of particles described by a kappa distribution can be accurately approximated by a weighted sum of Maxwell-Boltzmann distributions. We apply this method to modeling collision processes in kappa-distribution plasmas, with a particular focus on atomic processes important for solar physics. The relevant collision process rate coefficients are generated by summing appropriately weighted Maxwellian rate coefficients. This method reproduces the rate coefficients for a kappa distribution to an estimated accuracy of better than 5%. This is equal to or better than the accuracy of rate coefficients generated using "reverse engineering" methods, which attempt to extract the needed cross sections from the published Maxwellian rate coefficient data and then reconvolve the extracted cross sections with the desired kappa distribution. Our approach of summing Maxwellian rate coefficients is easy to implement using existing spectral analysis software. Moreover, the weights in the sum of the Maxwell-Boltzmann distribution rate coefficients can be found for any value of the parameter kappa, thereby enabling one to model plasmas with a time-varying kappa. Tabulated Maxwellian fitting parameters are given for specific values of kappa from 1.7 to 100. We also provide polynomial fits to these parameters over this entire range. Several applications of our technique are presented, including the plasma equilibrium charge state distribution (CSD), predicting line ratios, modeling the influence of electron impact multiple ionization on the equilibrium CSD of kappa-distribution plasmas, and calculating the time-varying CSD of plasmas during a solar flare.

Influence of Multiple Ionization on Charge State Distributions

SynopsisWe describe the influence of electron-impact multiple ionization (EIMI) on the ionization balance of collisionally ionized plasmas. Previous ionization balance calculations have largely neglected EIMI. Here, EIMI cross-section data are incorporated into calculations of both equilibrium and non-equilibrium charge-state distributions (CSDs). For equilibrium CSDs, we find that EIMI has only a small effect. However, for non-equilibrium plasmas the influence of EIMI can be important. In particular, we find that for plasmas in which the temperature oscillates there are significant differences in the CSD when including versus neglecting EIMI. These results have implications for modeling and spectroscopy of impulsively heated plasmas, such as nanoflare heating of the solar corona.

INFLUENCE OF ELECTRON-IMPACT MULTIPLE IONIZATION ON EQUILIBRIUM AND DYNAMIC CHARGE STATE DISTRIBUTIONS: A CASE STUDY USING IRON

We describe the influence of electron-impact multiple ionization (EIMI) on the ionization balance of collisionally ionized plasmas. We are unaware of any previous ionization balance calculations that have included EIMI, which is usually assumed to be unimportant. Here, we incorporate EIMI cross-section data into calculations of both equilibrium and non-equilibrium charge-state distributions (CSDs). For equilibrium CSDs, we find that EIMI has only a small effect and can usually be ignored. However, for non-equilibrium plasmas the influence of EIMI can be important. In particular, we find that for plasmas in which the temperature oscillates there are significant differences in the CSD when including versus neglecting EIMI. These results have implications for modeling and spectroscopy of impulsively heated plasmas, such as nanoflare heating of the solar corona.

Electron impact multiple ionization

We present theoretical calculations of electron impact multiple ionization of rare gases (single to quintuple for Ne, Ar, Kr and Xe). The theoretical model used is the CDW-EIS, adapted for electron impact, and the first Born approximation for the high impact energies (E>0.6 keV). The results presented here take into account the direct and the post-collisional ionization. The latter by including experimental branching ratios of Auger type processes. This formalism describes the experimental data quite well. In the case of Kr and Xe we obtain good tendency even for sextuple ionization.

Formation, structure, and dissociation dynamics of CO2q+(q≤3) ions due to impact of 12-keV electrons

The electron-impact multiple ionization and subsequent dissociation of CO${}_{2}$ is studied for 12-keV electron energy using a linear time-of-flight mass spectrometer coupled with a multihit, position-sensitive detector. The complete as well as incomplete Coulomb explosion pathways for CO${}_{2}$${}^{2+}$ and CO${}_{2}$${}^{3+}$ ions are examined and identified. The kinetic energy release distributions for these precursor ions are obtained. The experimental kinetic energy release values for the complete Coulomb fragmentation channels are found to be overestimated by those calculated from the Coulomb explosion model. From the angular correlation studies, it is inferred that bent geometrical states are involved for most of the fragmentation channels of CO${}_{2}$${}^{2+}$ and CO${}_{2}$${}^{3+}$ ions. The concerted and/or sequential nature of all the dissociation pathways is also assigned. This study provides the first results on energetics associated with the charge separation in dissociative ionization of CO${}_{2}$ under the impact of electrons at a subrelativistic energy.

Electron-impact ionization of atomic hydrogen: dynamical variational treatment

A simple and straightforward calculating scheme is proposed for electron-impact single and multiple ionization of atoms. The method is based on the application of the Hulthen-Kohn dynamical variational principle. An effective charge seen by the scattered electron is determined for a certain type of trial wave functions mathematically in a rigorous way excluding any empirical assumptions. Validity of the elaborated approach is assessed by calculating triply differential cross section (TDCS) for electron-impact ionization of hydrogen. It is shown that, inclusion of the effective charge into the calculation reduces height of a “binary peak” in comparison with the first Born approximation result. The height of a “recoil peak” depends on the sign of the effective charge. The calculated TDCS are compared with the available experimental data and with the results of sophisticated theories and agreement is found.

Comment on ‘Multiple ionization of helium and krypton by electron impact close to threshold: appearance energies and Wannier exponents’

We comment on recent measurements of electron-impact multiple ionization probabilities in the vicinity of threshold. Our conclusion is that these measurements are not inconsistent with the Wannier–Geltman nth power limiting threshold law.

Ionization cross section ratios of rare-gas atoms(Ne, Ar, Kr and Xe) by electron impact from thresholdto 1 keV

Electron impact multiple ionization relative cross sections ofrare gas atoms (Ne, Ar, Kr and Xe) have been measured using apulsed electron beam and a pulsed ion extraction combined witha time-of-flight analysis of the charge. The measurements covera larger range of energies and charges than in earlierexperiments, from threshold to 1 keV and from charge n = 1 to 4 (Ne),5 (Ar), 7 (Kr) and 6 (Xe). The average number(γ) of electrons ejected from the atom per ionizationevent is calculated and used to evaluate the contributions ofthe inner-shell processes. The results are also compared withthose in the case of photon impact. As regards the majorions produced, relative uncertainty as low as 1.3% for theionization cross section ratios is achieved for all the samplegases, except near threshold. As for the γ-values,relative uncertainty is estimated to be as low as 1.2%.

Recent results on multiple ionization and fragmentation of negatively charged fullerene ions by electron impact

Employing the dynamic crossed-beams technique, the absolute cross sections of the electron-impact multiple ionization and fragmentation of mass-selected negatively charged fullerene ions C m − → C m−n 2+ (m=60, 70, 84; q=1, 2, 3; n=0, 2, 4) were measured. The electron energy varied from the respective threshold up to 1 keV. A scaling law was observed for the cross-section magnitude as a function of the fullerene size m and the charge state q of product ions. The data indicate that different mechanisms account for the detachment of an extra electron from the negatively charged fullerene and the formation of a positively charged ion, respectively. Moreover, the multiple ionization of a fullerene anion is found to be a sequential process. A novel ionization mechanism is proposed which might be expected to be valid for all negatively charged molecular or cluster ions able to shield the attached electron from the incident electron.

Ionization and Fragmentation of Fullerene Ions by Electron Impact

Absolute cross sections for the electron-impact multiple ionization and fragmentation of negatively charged fullerene ions Cn–(n = 60, 70, 84) → Cn-mq+ (q = 1, 2, 3 and m = 0, 2, 4) have been measured for electron energies up to 1 keV. A scaling law has been observed for the magnitude of the ionization cross sections. Furthermore, the multiple ionization of a fullerene anion is found to be a sequential process. A novel ionization mechanism is proposed which can be expected to be valid also for other negatively charged molecular or cluster ions.

Calculation of cross sections and rate coefficients for the electron impact multiple ionization of beryllium, boron, carbon, and oxygen atoms

The semiclassical Deutsch-Märk (DM) formalism was used in a series of calculations of cross sections for the formation of Be m+ ( m = 1–4), B m+ ( m = 1–5), C m+ ( m = 1–6), and O m+ ( m = 1–8) ions by electron impact on the neutral atoms. Our calculated cross sections are compared with available experimental and other theoretical data and systematic trends in the data are highlighted. We also calculated a set of ionization rate coefficients on the basis of the calculated cross sections and Maxwell-Boltzmann electron energy distributions. In many applications, particularly applications relating to fusion plasmas, rate coefficients are more desirable than ionization cross sections.

Multiple ionization of CO due to electron impact

The absolute cross sections of all the possible dissociation channels following the electron-impact multiple ionization of CO have been measured. The cross sections of the channels corresponding to the production of ion pairs are measured by coincidence techniques. Those of the channels associated with neutral fragments are obtained indirectly. At high excitation energies, the total cross sections of different stages of ionization show an exponential decrease as the ionization stage increases. The cross sections of different channels reveal the internal dissociation dynamics of the dissociation following the multiple ionization of the molecules. The appearance potentials corresponding to different dissociation channels are also measured, which show that the ground states of triply and quadruply ionized CO are nearly Coulomb-like because the Coulomb interactions inside the molecules are stronger.

Ionization cross sections of C60 by fast electron impact

By means of a time-of-flight technique, we have measured cross sections for production of and ions from a gas-phase C60 target bombarded by 0.4-5.0 keV electrons. The results were in fairly good agreement with other data at overlapping energies below 1 keV. Semiclassical calculations of the single-ionization cross sections were also performed up to 10 keV using the Deutsch-Märk formula proposed for the molecule. A fairly good agreement between the experimental and theoretical cross sections was obtained both in magnitude and in energy dependence. It was found that the double and triple ionization cross sections both decrease monotonically and exhibit no hump structure, indicating that the inner-shell ionization does not play an important role in electron-impact multiple ionization of C60.

Single to quadruple ionization ofCO2due to electron impact

The electron-impact multiple ionization and the subsequent dissociation of ${\mathrm{CO}}_{2}$ have been studied for electron energies from the threshold to 600 eV. The dissociation channels of up to quadruply ionized carbon dioxide molecules have been identified. The absolute cross sections for the ion-pair dissociation channels in double, triple, and quadruple ionization of ${\mathrm{CO}}_{2}$ have been obtained. The absolute cross sections of the other channels involving neutral fragments are also derived. The experiment shows that the total cross section of single, double, and triple ionization decreases by at least an order of magnitude as the ionization stage increases by 1. By studying the structure of the islands in the covariance maps, we have concluded that one of the ${\mathrm{CO}}_{2}^{2+}$ dissociation channels ${\mathrm{CO}}_{2}^{2+}\ensuremath{\rightarrow}{\mathrm{C}}^{+}{\mathrm{}+\mathrm{O}}^{+}\mathrm{}+\mathrm{O}$ is dominated by the process of secondary decay. The dissociation channel ${\mathrm{CO}}_{2}^{2+}\ensuremath{\rightarrow}2{\mathrm{O}}^{+}\mathrm{}+\mathrm{C}$ is a concerted process. The three-body dissociation channels of triply ionized carbon dioxide are found to be dominated by concerted processes no matter how the charges are distributed on the fragments. The momentum distribution on the fragments can only be explained by the charge mobility during the dissociation process of the triply ionized molecules. The metastable decay of ${\mathrm{CO}}_{2}^{2+}$ is also observed directly.

Electron-impact multiple ionization of singly and multiply charged titanium ions

Using the crossed-beams technique the following absolute cross sections have been measured for the reaction : <PRE/> double ionization triple ionization quadruple ionization . Measurements for high charge states and ionization degrees, respectively, show significant contributions of inner-shell processes which partly dominate the respective cross section. The results are compared with the scaling laws of Fisher et al and the semiempirical formula published by Shevelko and Tawara, respectively.

Electron-impact multiple ionization of singly and multiply charged molybdenum ions

Cross sections for electron-impact double ionization of ions in charge states q = 1-6 as well as triple ionization for charge states q = 1-4 have been measured using the crossed-beams technique covering the entire range from the respective threshold up to energies well beyond maximum. The results are compared with the scaling law of Fisher et al and the semi-empirical formula published by Shevelko and Tawara, respectively. A comparison between experimental data and those formulae shows that a further improvement of the semi-empirical approaches is necessary. Together with previously obtained data for single ionization of molybdenum ions, the measured cross sections are used to study the influence of multiple ionization on the charge-state evolution if molybdenum ions are exposed to an electron flux at 700 eV energy.

A scaling of multiple ionization cross sections

On the basis of average experimental data we demonstrate scaling laws of electron-impact multiple ionization cross sections and propose expressions for the cross sections for arbitrary atoms and ions.

Resonances in the electron-impact single and multiple ionization of ions

Cross sections for electron-impact single ionization of Li-like ions B2+, C3+, N4+, O5+ and F6+ and for n-fold ionization of Li+ (n=l), Na+ (n=l), K+ (n=1,2,3), Rb+ (n=1,2,3), Cs+ (n=l,2,3,4) andBa+ (n=l,2,3,4) have been measured with extremely high precision (lowest limit of statistical uncertainties as low as 0.01% ). Detailed studies of indirect ionization mechanisms proceeding via multiply-excited intermediate states could be carried out.