Atomic Orbital Close-coupling Calculations Research Articles

Benchmark n ℓ-resolved Cross Sections of Single and Double Charge Exchange Processes in 1.67–20 keV u−1 C4+ Collisions with He

State-resolved charge exchange (CX) cross sections are of the utmost importance for modeling related photon emissions existing in a broad range of astrophysical environments. With the cold-target recoil-ion momentum spectroscopy, we determined with high accuracy the state-resolved single and double CX cross sections at the quantum orbital angular momentum level for solar wind ion C4+ collisions with He in an energy range of 1.67–20 keV u−1, which allow one to benchmark the CX calculations in great detail, and to test the applicability of the analytical n- and ℓ-distribution models widely adopted by the astrophysical community. We found that the present measurements are well reproduced by the most recent state-of-the-art atomic–orbital close-coupling calculations. However, the CX models failed to give a consistent description on the measured ℓ distributions. The present work reveals that the velocity and collision partner species dependence effects as well as electronic correlations for multielectron processes should be included in an improved model. Alternatively, in future modeling to interpret high-resolution astrophysical observations the more elaborate quantum-mechanical calculations may be resorted to with confidence.

State-selective electron capture in collisions of fully stripped neon ions with ground-state hydrogen

Electron capture and ionisation in bare neon ion collisions with ground-state atomic hydrogen are modelled over the energy range from 1 to 2000 keV/u using the two-center semiclassical wave-packet convergent close-coupling method. The calculated total electron-capture cross section agrees very well with the molecular and atomic orbital close-coupling calculations at low and intermediate energies. Our results slightly overestimate the experimental results by Meyer et al [1985 Phys. Rev. A 32 3310], but underestimate the measurements by Panov et al [1983 Phys. Scr. T3 124] available only below 10 keV/u. At higher energies, where there are no measurements, the results also agree very well with the classical trajectory Monte-Carlo results. Partial n and nl-resolved electron-capture cross sections, important for fusion plasma diagnostics, have also been calculated for final states up to n = 10, where n and l are the final state principal and angular momentum quantum numbers, respectively. The results are generally in good agreement with the atomic calculations. However, due to the finer energy grid used, we are able to detect pronounced oscillations in the state-selective cross sections for n ⩾ 8 at energies below 10 keV/u. Our results for the total ionisation cross section are overall in good agreement with the latest classical trajectory Monte-Carlo results.

Population of the states in collisions of mixed‐state (1s21S,1s2s3S) B3+ and C4+ ion beams with He and H2 targets

Auger KLn lines are observed in high‐resolution electron spectra obtained in collisions of mixed‐state (1s21S,1s2s3S) He‐like beams of 4 MeV B3+ with H2 and 6 MeV C4+ with He targets. Supporting atomic structure calculations show these lines to correspond to doubly excited states, which can be readily populated by electron transfer to the component of the mixed‐state beam. They thus provide indirect evidence for the existence of the corresponding KLn quartet states, similarly produced, even though their weak Auger decay does not allow for their direct observation in the electron spectra. These KLn quartet states mostly decay in a cascade chain of strong radiative E1 transitions, eventually terminating at the state, which is thus additionally enhanced. An upper limit on the state population due to cascades is obtained by assuming a statistical production of KLn quartet to doublet states followed by a 100% cascade feeding of the state. Our estimated upper limit is supported by our absolute cross section measurements and corresponding three‐electron atomic orbital close coupling calculations in progress. Results to date are presented and discussed.

Charge transfer and ionization in collisions of O8+ions with excited He atoms

Two-centre atomic orbital close-coupling calculations are carried out for the cross sections of single electron capture and single ionization in O8+ + He(1s1s) and O8+ + He(1s3d) collisions in the ...

Calculations and analysis of cross sections required for argon charge exchange recombination spectroscopy

A large set of calculations has been carried out providing a basis for diagnostics of fusion plasmas through emission resulting from radiative de-excitation following charge transfer between hydrogen and highly charged argon ions, so-called argon charge exchange recombination spectroscopy. These results have been obtained using the classical trajectory Monte Carlo (CTMC) method to treat charge transfer to states with principal quantum numbers up to 30 or more. Nine collision energies between 13.3333 and 250 keV/u pertinent to neutral beam injection have been considered for Arq+ (q = 15–18) colliding with atomic hydrogen in both the ground and metastable states. Atomic orbital close coupling calculations have also been undertaken in order to provide a fully quantum mechanical test of the CTMC results for Ar18+ + H(1s) collisions. The results of the calculations are discussed here and the full set of data is made available through a web posting.

Charge exchange in Be4+–H(n = 1, 2) collisions studied systematically by atomic-orbital close-coupling calculations

Charge exchange in Be4+–H(n = 1, 2) collisions was studied using the atomic-orbital close-coupling formalism in its impact parameter description and applying electron translational factors. Calculations were carried out in the energy range of 1–750 keV amu−1 with fully stripped beryllium ions impacting on atomic hydrogen in its ground state (1s) and in the excited n = 2 states. An optimized description of both collision centres was determined by analysing the convergence of the total cross sections and also by comparison with other theoretical approaches. This optimized description consists of up to 170 basis states involving hydrogen-like states and pseudostates. We present total, n-resolved as well as nℓ-resolved cross sections. The latter are needed to evaluate the emission cross sections in two limiting collisional plasma environments, i.e. single-collisional and multi-collisional. The calculated emission cross sections are compared with experimental data from the fusion experiment JET. Taking the experimental environment and certain characteristics of the theoretical methods into account, the agreement can be considered to be quite good.

Database for inelastic collisions of sodium atoms with electrons, protons, and multiply charged ions

The available experimental and theoretical cross section data for inelastic collision processes of ground (3s) and excited (3p, 4s, 3d, 4p, 5s, 4d, and 4f) state Na atoms with electrons, protons, and multiply charged ions have been collected and critically assessed. In addition to existing data, electron-impact cross sections, for both excitation and ionization, have been calculated using the convergent close-coupling approach. In the case of proton-impact cross section, the database was enlarged by new atomic-orbital close-coupling calculations. Both electron-impact and proton-impact processes include excitation from the ground state and between excited states ( n = 3–5). For electron-impact, ionization from all states is also considered. In the case of proton-impact electron loss, cross sections (the sum of ionization and single-electron charge transfer) are given. Well-established analytical formulae used to fit cross sections, published by Wutte et al. and Schweinzer et al. for collisions with lithium atoms, were adapted to sodium. The “recommended cross sections” for the processes considered have been critically evaluated and fitted using the adapted analytical formulae. For each inelastic process the fit parameters determined are tabulated. We also present the assessed data in graphical form. The criteria for comprehensively evaluating the accuracy of the experimental data, theoretical calculations, and procedures used in determining the recommended cross sections are discussed.

Charge transfer in slow collisions ofO8+andAr8+ions withH(1s)below2keV∕amu

We calculated the charge-transfer cross sections for ${\mathrm{O}}^{8+}+\mathrm{H}$ collisions for energies from $1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{amu}$ to $2\phantom{\rule{0.3em}{0ex}}\mathrm{keV}∕\mathrm{amu}$, using the recently developed hyperspherical close-coupling method. In particular, the discrepancy for electron capture to the $n=6$ states of ${\mathrm{O}}^{7+}$ from the previous theoretical calculations is further analyzed. Our results indicate that at low energies (below $100\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{amu}$) electron capture to the $n=6$ manifold of ${\mathrm{O}}^{7+}$ becomes dominant. The present results are used to resolve the long-standing discrepancies from the different elaborate semiclassical calculations near $100\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{amu}$. We have also performed the semiclassical atomic orbital close-coupling calculations with straight-line trajectories. We found the semiclassical calculations agree with the quantal approach at energy above $100\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{amu}$, where the collision occurs at large impact parameters. Calculations for ${\mathrm{Ar}}^{8+}+\mathrm{H}$ collisions in the same energy range have also been carried out to analyze the effect of the ionic core on the subshell cross sections. By using diabatic molecular basis functions, we show that converged results can be obtained with small numbers of channels.

Proton-impact excitation of laser-excited lithium atoms

A time-dependent solution of the Schr\"odinger equation on a three-dimensional lattice is used to calculate proton-impact excitation cross sections for both the ground $(2s)$ and first excited $(2p)$ states of the neutral lithium atom. Total cross sections for the $2\stackrel{\ensuremath{\rightarrow}}{s}3l$ and $2\stackrel{\ensuremath{\rightarrow}}{p}3l$ excitations are compared with atomic-orbital close-coupling calculations at incident energies of 15--50 keV. In support of future experiments involving crossed ion, atom, and laser beams, total aligned cross sections for the $2p\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}3l$ and $2p\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\pi}}3l$ excitations are presented over the same energy range. The ratio of aligned cross sections for certain excitations and incident energies is found to be almost a factor of 2.

DATABASE FOR INELASTIC COLLISIONS OF LITHIUM ATOMS WITH ELECTRONS, PROTONS, AND MULTIPLY CHARGED IONS

New experimental and theoretical cross-section data for inelastic collision processes of Li atoms in the ground state and excited states (up to n = 4) with electrons, protons, and multiply charged ions have been reported since the database assembled by Wutte et al. [Atomic Data and Nuclear Data Tables65, 155, 1997] was published. These new data were included in a process of critical data assessment and led to the creation of a new database for the modeling of energetic lithium beams probing fusion edge plasmas. The electron-impact part of the present database covers excitation and ionization, the data having been extended by advanced close-coupling calculations which provide a new standard of quality especially for transitions between excited states. The heavy-particle impact processes include excitation and electron removal (the sum of ionization and electron capture). Hitherto, ion-impact excitation cross sections for lithium (except for the main Li(2s → 2p) process) were based on scaling relations using the corresponding electron-impact cross sections. We have now performed large-scale atomic orbital close-coupling calculations for a large number of excitation processes as well as new measurements toward development of the new database. The recommended cross sections for the considered processes have been fitted to simple analytic expressions. The analytic-fit expressions and the tables of the parameters entering these analytic fits are here presented. We also present the recommended cross sections in graphical form together with the underlying experimental cross section data if available.

Effects of excitation and orbital alignment on electron transfer in -Na collisions

The effects of excitation and orbital alignment on the electron transfer process in - collisions are investigated experimentally and theoretically over a wide range of impact energies. Experimentally, the integral alignment parameter and the ratios between the integral transfer cross sections for targets to that for a target have been determined using an optically prepared target. The results are in good agreement with earlier data at lower energies of Campbell et al. Theoretically, the integral cross section results of our 26-state two-centre atomic orbital close-coupling calculations are in good agreement with all experimental data, including the absolute electron transfer cross section measurements of Daley and Perel. These processes are now well understood over more than three orders of magnitude for the impact energy range.

Low-energy total-electron-capture cross sections for fully stripped and H-like projectiles incident on H and H2.

Total-electron-capture cross sections are reported for fully stripped and H-like ions of C, N, O, F, and Ne colliding with atomic and molecular hydrogen targets in the energy range 0.18--8.5 keV/amu. At energies above 3 keV/amu the cross sections are approximately energy independent with magnitudes in the range (4--7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ ${\mathrm{cm}}^{2}$, and scale smoothly with projectile charge. Below 3 keV/amu the H-target cross sections for projectiles with even charge are smaller than those for projectiles of odd charge. For the ${\mathrm{H}}_{2}$-target data, the opposite trend prevails. For those systems where calculations exist, molecular orbital and atomic orbital close-coupling calculations are within 20% of the experimental results except at the lowest energies investigated.