Atomic Orbital Close-coupling Research Articles

Electron capture and excitation in intermediate-energy He2+–H(1s,2s) collisions

Abstract The semiclassical non-perturbative atomic orbital close-coupling approach has been employed to study the electron capture and excitation processes in He2+-H(1s) and He2+-H(2s) collision systems. In order to ensure the accuracy of our calculated cross sections, a large number of high excited states and pseudostates are included in the expansion basis sets which centered on target and projectile, respectively. The total and partial charge transfer and excitation cross sections are obtained for a wide-energy domain ranging from 1 to 200 keV/amu. The present calculations are also compared with the results from other theoretical methods. These cross section data is useful for the investigation of astrophysics and laboratory plasma.

Theoretical Study of Electron Capture, Excitation, and Ionization Processes in H+−H(2l) Collisions

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.

Cross sections in He+ + H collisions for the energy region 1–100 keV u−1

We have calculated the cross sections for the elastic, excitation, electron capture, and ionization processes in He+ + H collision using a semiclassical atomic orbital close-coupling method within two-electron treatment. The calculated data are compared with those of the experiments and previous theoretical calculations. The excitation cross sections to H(n = 2) states are in good agreements with the measurements of Geddes et al. The Balmer-alpha emission cross section of H is about half the size of the experimental data of Donnelly et al. The electron capture cross section is close to the experimental data of Lockwood et al and Olson et al. The ionization cross section is in accord with the experimental data of Hsu et al.

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.

Coherent treatment of transfer-excitation processes in swift ion-atom collisions

For more than 40 years since the first ion-atom collision investigations of the two-electron process of electron transfer with excitation and its resonant and nonresonant features, a satisfactory quantum mechanical treatment has been lacking. We present now such a comprehensive transfer excitation treatment using a three-electron atomic orbital close-coupling approach within a full configuration interaction formalism, exemplified by ${\mathrm{C}}^{4+}(1{s}^{2})+\mathrm{He}$ collisions at 0.5--18 MeV impact energies. The calculated cross sections for the production of ${\mathrm{C}}^{3+}(1s2{p}^{2}\phantom{\rule{0.16em}{0ex}}^{2}D)$, which shows the strongest resonance signature among the KLL Auger transitions, are found to be in excellent agreement with zero-degree Auger projectile spectroscopy measurements covering the maximum of the resonance peak and its high energy wing. At the lower energies, the theoretical results show a second maximum which is interpreted through a nonresonant one-step transfer excitation mechanism, never considered to date. The present, fully coherent, many-body treatment provides an important advance in the modeling and understanding of multielectronic processes in quantum systems under strong and ultrafast perturbations.

Total, state-selective, and angular-differential cross sections for electron capture in He2++H collisions in warm dense plasmas

The total, state-selective, and angular-differential cross sections for He2++H collision system in warm dense plasmas are studied by using the two-center atomic orbital close-coupling method in the energy range 0.1–300 keV/u. The calculations are performed for plasma density and temperature ranges ne ∼1018 to ∼1021 cm−3, Te = 0.3 eV–1.2 eV, typical for the H- and He-rich white dwarfs. The plasma environments are described by a unified screened potential involving electron degeneracy, finite-temperature gradient, and exchange-correlation effects. The results for H++H cases with the same plasma parameters are also presented for comparison to elucidate the discrepancies of plasma screening effects on the electron capture dynamics for collision systems with different nuclear symmetries. Moreover, classical Debye screening results are also given for comparison to clarify the effects of quantum correlations in warm dense plasmas on the electron capture dynamics. The present work is expected to provide theoretical and data support for the astrophysical plasmas.

State-resolved differential cross sections of single-electron capture in swift collisions ofC4+(1s2s3S) ions with gas targets

We report on double and single differential cross section measurements of the $1s2{s}^{2}\phantom{\rule{0.16em}{0ex}}^{2}S$, $1s2s2p\phantom{\rule{0.16em}{0ex}}^{2}P_{\ifmmode\pm\else\textpm\fi{}}$, and $1s2s2p\phantom{\rule{0.16em}{0ex}}^{4}P$ doubly excited states produced by single-electron capture in 6--15 MeV collisions of pre-excited ${\mathrm{C}}^{4+}(1s2s\phantom{\rule{0.16em}{0ex}}^{3}S)$ ions with ${\mathrm{H}}_{2}$, He, Ne, and Ar targets. Ab initio cross section calculations based on a three active electrons atomic orbital close-coupling approach are compared to the measurements for collisions with the lighter ${\mathrm{H}}_{2}$ and He targets, showing an overall good agreement. Theoretical details concerning Auger electron angular distributions, partial cross sections, impact parameter dependencies, and radiative cascade feeding effects are discussed. The populations of the $1s2s2p\phantom{\rule{0.16em}{0ex}}^{4}P$, $^{2}P_{\ensuremath{-}}$, $^{2}P_{+}$ multiplets concerning the spin symmetry are finally presented for the four collision systems and discussed following the comparisons between theory and experiment.

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.

Total and subshell-selective charge exchange cross sections in collisions of highly-charged Ne ions with atomic hydrogen

Total and subshell-selective charge exchange cross sections and the corresponding reaction rate coefficients for Neq+-H (q=6–10) collision systems are calculated by utilizing the two-center atomic orbital close-coupling (TC-AOCC) method at impact energy between 0.1 keV/u and 500 keV/u. Good agreements with the experimental and other theoretical results are found for the total charge transfer cross section in the considered energy range and for those of the dominant charge-exchange channels for the higher collision energies. These charge exchange cross section data are useful for understanding and modeling the X-ray emission in environments where charge transfer is an important mechanism generating this emission.

Atomic Data for Calculation of the Intensities of Stark Components of Excited Hydrogen Atoms in Fusion Plasmas

Motional Stark effect (MSE) spectroscopy represents a unique diagnostic tool capable of determining the magnitude of the magnetic field and its direction in the core of fusion plasmas. The primary excitation channel for fast hydrogen atoms in injected neutral beams, with energy in the range of 25–1000 keV, is due to collisions with protons and impurity ions (e.g., He 2 + and heavier impurities). As a result of such excitation, at the particle density of 10 13 –10 14 cm − 3 , the line intensities of the Stark multiplets do not follow statistical expectations (i.e., the populations of fine-structure levels within the same principal quantum number n are not proportional to their statistical weights). Hence, any realistic modeling of MSE spectra has to include the relevant collisional atomic data. In this paper we provide a general expression for the excitation cross sections in parabolic states within n = 3 for an arbitrary orientation between the direction of the motion-induced electric field and the proton-atom collisional axis. The calculations make use of the density matrix obtained with the atomic orbital close coupling method and the method can be applied to other collisional systems (e.g., He 2 + , Be 4 + , C 6 + , etc.). The resulting cross sections are given as simple fits that can be directly applied to spectral modeling. For illustration we note that the asymmetry detected in the first classical cathode ray experiments between the red- and blue-shifted spectral components can be quantitatively studied using the proposed approach.

Electron capture and 2s→2p excitation in Be3+-Li collisions

The electron capture and 2s→2p excitation processes in Be3+-Li collisions are investigated by the quantum-mechanical molecular orbital close-coupling (QMOCC) method and by the two-center atomic orbital close-coupling (TC-AOCC) method in the energy ranges 10−4–1.2 keV/u and 0.5–100 keV/u, respectively. Spin-resolved total, n-shell and state-selective electron capture cross sections are calculated with large expansion of the MO and AO basis sets. In the overlapping energy range the results of the two sets of calculations for the total and n = 4, 3-shell capture cross sections agree very well for both singlet and triplet channels. Good agreement in this energy range between the two calculations is obtained also for the spin-resolved cross sections except some weak reaction channels. It is found that the total and n = 4 shell singlet and triplet capture cross sections differ significantly from each other in the energy region below 0.1 keV/u, and especially for the 4l cross sections this difference becomes considerable at 1 keV/u. For the weak n = 3 and n = 2 capture channels the difference between singlet and triplet cross sections is much smaller. The excitation 2s-2p cross section for Li in this collision system has also been calculated and no significant difference between the singlet and triplet cross sections was found in the entire energy range considered.

Electron capture in collisions of Li3+ ions with ground and excited states of Li atoms**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300), the National Natural Science Foundation of China (Grant No. 11774037), International Atomic Energy Agency, China (Grant No. 23196/R0), and the Science Challenge Project of China (Grant No. TZ2016001).

The electron capture processes in collisions of Li3+ ion with Li(1s22s) and Li(1s22p0,1) are investigated by using the two-center atomic orbital close-coupling method in the energy range from 0.1 keV/u to 300 keV/u. The interaction of the active electrons with the target ion is represented by a model potential. The present results for the Li3+–Li(1s22s) system are compared with the available theoretical data and general agreement is obtained for the high collision energies. It is also found that the total and partial electron capture cross sections are sensitive to the initial charge cloud alignment in the low energy region.

Proton impact charge exchange and excitation cross sections for liquid Sn divertor studies

AbstractThe quantum dynamics of charge exchange (electron capture) and excitation processes in proton collisions with Sn atoms is studied for the first time by using the two‐centre atomic orbital close coupling method. The expansion basis includes the lowest nine states of singlet and triplet symmetry of Sn and all the states with n ≤ 8 of the H atom. The spin‐resolved state‐selective charge exchange (up to n = 5) and excitation cross sections are calculated in the energy range of 0.5 − 100 keV. Strong coupling between the electron capture and excitation channels is observed in the low‐energy (E ≤ 10 keV) region associated with the energy quasi‐resonance of some projectile and target states. The intensities of some strong Sn spectral lines are also calculated for a number of typical tokamak edge plasma temperatures.

Electron capture, excitation and ionization in H+–Be+ collisions

State-selective single electron capture, excitation and ionization processes in proton collisions with Be+(1s22s) and Be+(1s22p) ions are studied by using the quantum-mechanical molecular orbital (QMOCC) and the two-center atomic orbital close-coupling (TC-AOCC) methods in the combined energy range 0.01–300 keV/u. In the QMOCC calculations six 2Σ+ and three 2Π states are included in the expansion basis. The TC-AOCC expansion basis includes 35 discrete states centered on the proton and 182 states on Be2+ out of which 88 are continuum pseudostates. The atomic states on Be2+ are generated by a one-electron model potential for the electron interaction with Be2+ ion core that reproduces the exact energies with accuracy better than 0.5%. Total and state-selective electron capture and excitation cross sections to final states with n ≤ 4 are presented. The sum of the cross sections for the transitions to continuum pseudostates (ionization cross section) is also reported for both initial target states. The physical mechanisms involved in the dynamics of considered processes are discussed in detail at both low and high energies. The reported cross sections should be useful in the kinetic modeling and diagnostics of edge plasmas in present magnetic fusion experiments, as well as in the current ITER design, in which beryllium is used as first wall material.

Electron capture and excitation in H+ − Li+ collisions

The processes of state-selective electron capture and excitation in proton collisions with Li+(1s2 1S) and Li+(1s2s 1,3S) ions are studied by using the two-center atomic orbital close-coupling (TC-AOCC) methods in the energy range 2.5–800 keV. The interaction of the active electron with the Li2+ ion core is represented by model potentials that reproduce the energies of excited singlet and triplet states of Li+ with accuracy better than 2%. The expansion basis in the coupled state calculations includes all states with n ≤ 8 (in total 120 states) centered on each of the colliding centers. Total and state-selective electron capture and excitation cross sections to final states with n ≤ 4 are presented. The physical mechanisms involved in the dynamics of considered processes are discussed in detail. The reported cross sections should be useful in the kinetic modeling and diagnostics of fusion reactor plasmas with liquid lithium divertors.

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.

Electron capture and excitation in He+–He(1s2s1,3S) collisions

State-selective single-electron capture and excitation processes in collisions of He+ ions with metastable He(1s2s1,3S) excited atoms are investigated by using the two-center atomic orbital close-coupling method in the energy range 0.5–100 keV/u. The expansion basis includes all the states with n ≤ 9, lmax = 4 on the projectile and all the states with n ≤ 5, lmax = 4 on the target, when treating the electron capture and vice versa, when treating the ionization. One-electron model potentials for the singlet and triplet series of states have been used that reproduce the exact energies within an accuracy of 1%–2%. Spin-resolved electron capture and excitation cross sections to nl final states with n ≤ 4 are presented. The origin of differences in the magnitude and energy behavior of spin-resolved cross sections is discussed. The reported cross section results should be useful in the studies of properties of various laboratory and astrophysical helium plasmas.

Double Electron Capture in H^{+}+H^{-} Collisions.

We have investigated the double electron capture process in the H^{+}+H^{-} collision system for energies from 60eV to 20keV. Despite the apparent simplicity of this highly correlated system, all previous calculations fail to reproduce the experimental total cross sections. Moreover, the latter exhibit oscillations that have been previously attributed to quantum interferences between the gerade and ungerade ionic states of the transient molecule formed during the collision. For this process, we present the absolute cross sections obtained from a fully correlated two-active-electron semiclassical atomic-orbital close-coupling approach. Our results reproduce well the experimental data in both magnitude and shape. Furthermore, we demonstrate that the oscillations stem from coherence effects between double electron capture and other two-electron inelastic channels, namely the transfer-excitation processes. This alternative interpretation is supported by a Rosenthal-like model based on a molecular treatment of the collision. Our results shed new light on this old but challenging problem.

Electron capture, excitation and ionization processes in He2+–H collisions in dense quantum plasmas

Electron capture, excitation and ionization processes in He2+–H collisions taking place in quantum plasmas are studied by employing the two-center atomic orbital close coupling (TC-AOCC) method. The Debye-Huckel-cosine (DHC) potential is used to describe the plasma screening effects on the Coulomb interaction between charged particles. The properties of eigenenergies of hydrogen-like atom with DHC potential are investigated as function of the screening length of the potential. It is found that the binding energies of nl states decrease with decreasing the screening length of the potential. The dynamics of excitation, electron capture and ionization processes in He2+–H collision system is investigated when the screening length of the potential varies for a wide collision energy range. The TC-AOCC cross sections are compared with those for the pure Coulomb potential and, for the total electron capture, with the results of classical trajectory Monte Carlo method.

Proton scattering from excited states of atomic hydrogen

Wavepacket continuum-discretisation approach is used to calculate excitation, ionization and electron-capture (ec) cross sections for proton collisions with n = 2 states of atomic hydrogen, where n is the principal quantum number. The approach assumes a classical motion for the projectile and is based on the solution of the three-body Schrödinger equation using the two-center expansion of the total scattering wave function. The scattering wave function is expanded in an orthonormal basis set built from negative-energy eigenstates and wavepacket pseudostates representing the continuum of both the target atom and the atom formed by the projectile after capturing the electron. With a sufficiently large basis, due to the strong coupling between channels, the method produces converged cross sections for direct-scattering, ionization and ec processes simultaneously. For the quasi-elastic transitions, where both orbital and magnetic quantum numbers change, the integrated cross section is infinite. Nevertheless, the corresponding transitions probabilities are finite at any given impact parameter, indicating that the angular differential cross sections can be measured. Calculated cross sections for scattering on the metastable 2s state are compared with other theoretical results obtained using atomic-orbital close-coupling and classical-trajectory Monte Carlo approaches. Considerable disagreement with previous calculations has been found for some transitions at various incident energies.