Xenon charge exchange cross sections for electrostatic thruster models

Highly charged xenon (35+ to 46+) and thorium (72+ to 79+) ions were produced in an Electron Beam Ion Trap (EBIT). The ions were extracted from EBIT in a short pulse. Ions of one charge state were selected using an electromagnet. The ions were recaptured at low energy in a cryogenic Penning trap (RETRAP). As the ions captured electrons from molecular hydrogen, populations of the various charge states were obtained by measuring the image currents induced by the ions on the electrodes of the trap. Data on the number of ions in each charge state vs. time were compared to theoretical rate equations in order to determine the average charge exchange rates. These rates were compared to charge exchange rates of an ion with a known charge exchange cross section (Ar{sup 11+}) measured in a similar manner in order to determine the average charge exchange cross sections for the highly charged ions. The energy of interaction between the highly charged ions and hydrogen was estimated to be 4 eV in the center of mass frame. The mean charge exchange cross sections were 9 {times} 10{sup {minus}14} cm{sup 2} for Xe{sup 43+} to Xe{sup 46+} and 2 {times} 10{sup {minus}13} cm{sup 2} for Th{sup 73+} to Th{sup 79+}. Double capture was approximately 20--25% of the total for both xenon and thorium. A fit indicated that the cross sections were approximately proportional to q. This is consistent with a linear dependence of cross section on q within the measurement uncertainties.

Charge exchange, or electron capture, between highly charged ions and atoms and molecules has been considered as one of important mechanisms controlling soft X-ray emissions in many astrophysical objects and environments. However, to model charge exchange soft X-ray emission, astrophysicists commonly use principal quantum number <i>n</i> and angular momentum quantum number<i>l</i> resolved state-selective capture cross section data, which are usually obtained by empirical and semi-classical theory calculations. The accuracy of the theoretical model is the key to constructing an accurate X-ray spectrum. With a newly-built cold target recoil ion momentum spectroscopy apparatus, we perform a series of precise state-selective cross section measurements on Ne<sup>8+</sup> ions’ single electron capture with He targets, with the projectile energy ranging from 1.4 to 20 keV/u. The experimentally measured Q value spectrum shows that the process of electron captured to state of Ne<sup>7+</sup> with <i>n</i> = 4 is the main reaction channel, and that with <i>n</i> = 3 and 5 are the small reaction channels. Using Gaussian curve to fit the area of each channel on the Q value spectrum and normalizing the area of all channels, we obtain the <i>n</i>-resolved relative state-selective cross section. By comparing the measured relative cross sections with the results calculated by the multichannel Landau-Zener method and molecular Coulomb over-barrier model, significant difference among the strengths of small reaction channels is found. Specifically, the multichannel Landau-Zener method overestimates the contribution of <i>n</i> = 2 channel and <i>n</i> = 3 channel, and underestimates the contribution of <i>n</i> = 5 channel. The molecular Coulomb over-barrier model overestimates the contribution of <i>n</i> = 5 channel and underestimates the contribution of <i>n</i> = 3 channel. The significant difference between the theoretical model calculation and experimental measurement is due to the limitations of semiclassical theoretical method and classical theoretical method. Furthermore, with <i>l</i> distribution models commonly used in the astrophysical literature, including the statistical model, separable model, Landau-Zener-I model, Landau-Zener-II model and even model, we calculate the soft X-ray emissions in the charge exchange between 1.6 and 2.4 keV/u Ne<sup>8+</sup> and He. It is found that the calculated intensities of X-ray spectra significantly deviate from the existing measurements, and only the separable model can partly match the laboratory simulated solar wind charge exchange X-ray measurement. Furthermore, we find that the intensity of the charge exchange X-ray emission spectrum measured experimentally is dependent on the collision energy, while the emission spectrum calculated based on the model seems to be unchanged with the increase of the collision energy. These results indicate that if the classical and semi-classical models are applied to the astrophysical plasma for studying diffusive soft X-ray background, the obtained parameters of the astrophysical plasma will be inaccurate.

The ratios of the differential cross sections (DCS's) for excitation of the first, second, and third vibrational states of H2 in its ground electronic state to the elastic DCS have been measured as a function of scattering angle in the 10°–80° range and impact energy in the 7–81.6-eV range. From these ratios the DCS's corresponding to transitions from the ground to the first two vibrationally excited levels (fundamental and first overtone bands) were obtained by utilizing the elastic cross sections determined in the previous paper (II). In addition, the DCS for excitation of the second overtone band was determined for an impact energy of 10 eV. By angular extrapolation and integration of the DCS's the integral cross sections for the vibrational excitations were also determined. In addition, all these cross sections have been calculated using a quantum-mechanical method based on potential scattering in a plane wave scattering approximation which is described in Part I of this series. The present experimental and theoretical cross sections and previous measurements and calculations are compared. The calculated DCS ratios and the DCS's themselves for the fundamental excitation are in good agreement with experiment at 7 and 10 eV; however, at higher energies the calculated DCS's are generally larger than the experimental ones, at some angles by as much as a factor of 10. The calculated ratio of the DCS for the fundamental excitation to the elastic DCS shows a minimum as a function of angle, in qualitative agreement with the experimental results in the 13.6–81.6-eV energy range. The experimental DCS's for vibrational excitation also show a deep minimum. For excitation of the first overtone vibration, the experimental ratios are an order of magnitude larger than the calculated ones at low energy but in better agreement for the magnitude at higher energy. This discrepancy at low energies is explained in terms of resonance scattering. Our experiments are in good agreement with those of others in the few (low energy) cases where comparison is possible.

The energy dependence of the total cross section for symmetric charge exchange in helium is measured in the range from 400-2000 eV. Beam-attenuation techniques are used, and all measurements are made on the forward-scattered ions and the high-energy neutrals resulting from the charge exchange. Cross-section values are given at 100-eV intervals, and the results show a cross section decreasing as the energy increases, with a value at 1000 eV of 1.04 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}15}$ ${\mathrm{cm}}^{2}$. The absolute cross sections are accurate to \ifmmode\pm\else\textpm\fi{} 12%. Relative cross-section values accurate to \ifmmode\pm\else\textpm\fi{} 6% are reported.

Semiclassical calculations of differential cross sections for rotational/vibrational transitions in Li + + N 2

Charge exchange from doubly charged rare gas cations to simple diatomics proceeds with a large cross section and results in populations of many vibrational and electronic product states. The charge exchange between Xe(2+) and N2, in particular, is known to create N2 (+) in both the A and B electronic states. In this work, we present integral charge exchange cross section measurements of the Xe(2+) + N2 reaction as well as axial recoil velocity distributions of the Xe(+) and N2 (+) product ions for collision energies between 0.3 and 100 eV in the center-of-mass (COM) frame. Total charge-exchange cross sections decrease from 70 Å(2) to about 40 Å(2) with increasing collision energy through this range. Analysis of the axial velocity distributions indicates that a Xe(2+) - N2 complex exists at low collision energies but is absent by 17.6 eV COM. Analysis of the axial velocity distributions reveals evidence for complexes with lifetimes comparable to the rotational period at low collision energies. The velocity distributions are consistent with quasi-resonant single charge transfer at high collision energies.

In order to apply to neutral beam etching, several hundred eV neutral beams have been generated by charge exchange reaction using a magneto-microwave plasma ion source. The charge exchange cross sections for Ar+ and Kr+ are unexpectedly small, whereas the cross section for Ne+ of 300 eV is 1.7×10−15 cm2 in good agreement with published results. The small cross sections for Ar+ and Kr+ in the present experiments are explained in terms of a nonresonant charge exchange scheme. The capacitance–voltage (C–V) measurements show that the radiation damage to SiO2/Si by Ne0 neutral beam bombardment is much less than those by Ne+ ion beam and by vacuum ultraviolet photons. Consequently, the neutral beam process is a promising method for charge-free and low-damage surface processes.

Cross sections for single electron capture (SEC), or charge exchange (CX), in collisions of Ne(8–10)+ and Mg(8–12)+ with H and He, are computed using an approximate multichannel Landau–Zener (MCLZ) formalism. Final-state-resolved cross sections for the principal (n), orbital angular momentum (ℓ), and where appropriate, total spin angular momentum (S) quantum numbers are explicitly computed, except for the incident bare ions Ne10+ and Mg12+. In the latter two cases, -resolution is obtained from analytical ℓ-distribution functions applied to n-resolved MCLZ cross sections. In all cases, the cross sections are computed over the collision energy range 1 meV/u to 50 keV/u with LZ parameters estimated from atomic energies obtained from experiment, theory, or, in the case of high-lying Rydberg levels, estimated with a quantum defect approach. Errors in the energy differences in the adiabatic potentials at the avoided crossing distances give the largest contribution to the uncertainties in the cross sections, which are expected to increase with decreasing cross section magnitude. The energy differences are deduced here with the Olson–Salop–Tauljberg radial coupling model. Proper selection of an ℓ-distribution function for bare ion collisions introduces another level of uncertainty into the results. Comparison is made to existing experimental or theoretical results when available, but such data are absent for most considered collision systems. The -resolved SEC cross sections are used in an optically thin cascade simulation to predict X-ray spectra and line ratios that will aid in modeling the X-ray emission in environments where CX is an important mechanism. Details on a MCLZ computational package, Stueckelberg, are also provided.

Calculated total, differential, and momentum-transfer cross sections are reported for the vibrationally elastic scattering of electrons from ${\mathrm{H}}_{2}$O and ${\mathrm{NH}}_{3}$ molecules in the range of energy 0.5--20 eV. The total cross sections are approximated by a sum of the rotationally elastic ones and the rotational transition from ground to first excited state (00\ensuremath{\rightarrow}10). The first-order Born approximation with the rotating-molecule model is used in the calculation of the first rotational excitation cross section. The experimental value of the dipole moments of ${\mathrm{H}}_{2}$O and ${\mathrm{NH}}_{3}$ are used in this step of the calculation. Spherically approximate molecular wave functions are applied to calculate the spherical part of the interactions of the incident electron with the molecule and the rotationally elastic-scattering cross section, in which the static and exchange interactions are calculated exactly within the accuracy of the molecular wave function and a parameter-free correlation-polarization potential is used to account for the polarization effect. The agreement of the differential cross sections with the experimental data is good at small angles and reasonably good at intermediate and large angles. Good agreement with measured values is obtained for the momentum-transfer cross sections. Total cross sections are reported with theoretical results on the e-${\mathrm{NH}}_{3}$ system below 10 eV. The possible sources of the discrepancies between the current theoretical and experimental results are analyzed for the total cross sections at very low energies by a quantitative consideration of the contributions of very strong forward scattering at near-zero angles to the total cross sections.

Symmetric (homonuclear) charge transfer between completely stripped projectiles and hydrogenlike atoms is studied by means of the second-order Born approximation (CB2) with the correct boundary conditions. Along the integration path, the transition amplitude ${\mathit{T}}_{\mathit{i}\mathit{f}}^{\mathrm{CB}2}$ exhibits so-called movable singularities, such as branch points and poles. A powerful method is presented which demonstrates that these singularities are integrable, not only for the resulting cross sections, but also for every individual matrix element. The resulting algorithm is very efficient, since the exact differential cross sections of the CB2 method are readily obtained through only two-dimensional numerical quadratures. The present theory is applied to symmetric resonant charge exchange in ${\mathrm{H}}^{+}$+H(1s)\ensuremath{\rightarrow}H(1s)+${\mathrm{H}}^{+}$ collisions at several impact energies, and the results are found to be in satisfactory agreement with the experimental data of Martin et al. [Phys. Rev. A 23, 3357 (1981)] and Vogt et al. [Phys. Rev. Lett. 57, 2256 (1986)].

A high-and-flat efficiency moderated neutron detection array of 3He counters has been recently developed for photoneutron cross section measurements at the future ELI-NP gamma-ray beam source. We have designed a three rings geometry of 31 counters with a ˜37% efficiency flat within 5% in the 10 keV to 5 MeV neutron energy interval. A commissioning experiment was performed using proton beams delivered by the 9 MV Tandem accelerator of IFIN-HH. We measured the neutron production cross sections for proton induced reactions on nat Cu and 27Al. The (p, xn) reactions on nat Cu were investigated in the 4.5 MeV to 14 MeV proton energy range with 250 keV steps, using pulsed and continuous proton beams. The low energy measurements below 10 MeV served to validate the detection efficiency calibration against well-known natCu(p, n) cross sections. The 27Al(p, n) reaction was investigated in the 5.8 MeV to 6.75 MeV energy range with 5 keV steps. Preliminary cross section results are here compared with preceding data.

Relative emission cross sections have been measured for spectral lines in the vacuum ultraviolet region which are produced by collisions of ${\mathrm{He}}^{+}$ with Ar over a range of energies from threshold to 10 keV. The lines investigated arise from the following excited states of Ar and ${\mathrm{Ar}}^{+}$: for Ar, $3{p}^{5}4s[^{1}P,^{3}P]$; for ${\mathrm{Ar}}^{+}$, $3s3{p}^{6}^{2}S$, $3d^{2}P$, $3d^{2}D$, $4s^{2}P$, and $4{s}^{\ensuremath{'}}^{2}D$. Charge exchange at low collision energies is dominated by transfer into the $3s3{p}^{6}$ states. The cross section for exciting this configuration rises rapidly from threshold at 4.7 eV to a low-energy maximum which occurs at 11.3 eV. By normalizing our data to the absolute emission cross section which has been determined by De Heer et al. at a collision energy of 2 keV, it is found that the cross section for exciting the $3s3{p}^{6}$ configuration is 5.4 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at the low-energy maximum. Oscillations are observed in several of the emission cross sections which indicate interferences between the wave functions of one or more of the excited states of the quasimolecule.

We report results for positron scattering by ground-state atomic hydrogen in the energy range 0 to 80 eV. The calculations have been performed in an 18-state Ps(1s, 2s, 3s, 4s, 2p, 3p, 4p, 3d, 4d)+H(1s, 2s, 3s, 4s, 2p, 3p, 4p, 3d, 4d) approximation where the pseudostates (denoted by a bar) have been taken from Fon et al. (1981). Cross sections are presented for elastic scattering, positronium formation, total scattering and ionization. The elastic scattering results are in good agreement with accurate variational numbers at low energies and with other sophisticated, but very different, theoretical approximations at higher energies. We estimate that the elastic cross section is now known to better than 10%. The cross section for positronium formation is dominated by capture into the 1s state and is in fairly good agreement with the measurements of Weber et al. (1994). The results for the total cross section are generally consistent with the upper and lower bounds of Zhou et al. (1994) but are a little larger than other theoretical estimates at the higher energies. There is also a general theoretical problem concerning the degree to which the total cross sections for electrons and positrons merge at energies above 31 eV. The calculated ionization cross section is in agreement with the measurements of Jones et al. (1993).

theoretical rate equations in order to determine the average charge exchange rates. These rates were compared to charge exchange rates of an ion with a known charge exchange cross section (Ar{sup 11+}) measured in a similar manner in order to determine the average charge exchange cross sections for the highly charged ions. The energy of interaction between the highly charged ions and hydrogen was estimated to be 4 eV in the center of mass frame. The mean charge exchange cross sections were 9 {times} 10{sup {minus}14} cm{sup 2} for Xe{sup 43+} to Xe{sup 46+} and 2 {times} 10{sup {minus}13} cm{sup 2} for Th{sup 73+} to Th{sup 79+}. Double capture was approximately 20--25% of the total for both xenon and thorium. A fit indicated that the cross sections were approximately proportional to q. This is consistent with a linear dependence of cross section on q within the measurement uncertainties.

The processes of single-electron charge exchange, excitation, and ionization during proton impact on H(2l) are investigated. We employ two different theoretical methods that are suitable for different collision energy regions: the full quantum-mechanical molecular orbital close-coupling method for energies from 0.001 to 1 keV u−1 and the two-center atomic orbital close-coupling (TC-AOCC) method for energies between 0.3 and 100 keV u−1. For charge exchange and excitation processes, the total and nl-resolved cross sections to the final reaction channels of H (nl, n = 1–4) have been obtained over a broad energy region. Moreover, the ionization cross sections in the TC-AOCC calculation are also reported for both H(2s) and H(2p) initial target states. The present results are all compared with those from other sources when available. It is found that the magnitude and energy behavior of nl-resolved excitation cross sections for H+–H(2p) collisions are significantly distinct from those of the H(2s) initial state in the entire energy range considered, particularly in the low-energy region. The energy behaviors of the nl-resolved charge exchange cross sections from the H(2p) initial state are similar to those from the H(2s) initial state, but their magnitudes are larger. The present accurate cross-section data are anticipated to provide insight into the research of astrophysics and controlled fusion plasmas.