Molecular-orbital Close-coupling Research Articles

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.

Theoretical investigation of electron capture processes in slow O7+–H collisions

Aims. The total and n-, l-, and S -resolved single-electron-capture cross sections for the collisions of O7+ with atomic hydrogen are studied in the energy region from 10−3eV u−1−5keV u−1. Methods. These state-selective cross sections were calculated by employing the full quantum-mechanical molecular-orbital close-coupling (QMOCC) method. The ab initio multireference single- and double-excitation configuration interaction approach, with optimized atomic basis sets to accurately describe the highly excited states, was used to obtain the adiabatic potentials and the radial and rotational coupling matrix elements that are required in the QMOCC calculation. Results. Our results are compared with other available theoretical and experimental data. The n = 5 manifold is the dominant reaction channel for the chasrge-transfer process for this collision system over the entire energy range, and our results agree better with the experimental data than the other theoretical results in the energy region in which they overlap because we included the necessary highly excited states in the expansion basis set. These charge-exchange cross-section data are useful for understanding and modeling the X-ray emission in astrophysical environments.

Elastic and electron capture processes in slow He+–He collision

Aims. The elastic and electron-capture processes of He+ ions with ground helium atoms are very important for studies in astrophysics. It is essential to have reliable state-selective charge transfer, elastic, and transport cross-sections, along with the corresponding reaction rate coefficient data, especially for low collision energies. Methods. We investigated the elastic and non-radiative electron-capture processes in He+(1s)–He(1s2) collisions are investigated employing the full quantum-mechanical molecular orbital close-coupling method. The adopted ab initio adiabatic potentials and coupling matrix elements were obtained by a multi-reference single- and double-excitation configuration interaction approach. Results. We computed the elastic, charge-transfer, and transport cross-sections in the energy range of 0.01–2500eVamu−1 and the reaction rate coefficient in the temperature range of 10–109 K. Good agreement was achieved when compared to the available experimental and theoretical results. Shape resonance, Regge, and Glory oscillations were also found in the elastic and charge transfer cross-sections in the energy region considered here.

Mutual neutralization in low-energy collisions of Na+ + H- ions

Abstract The low-energy mutual neutralization (MN) reactions Na+ + H- → Na(nl) + H have been studied by employing the full quantum-mechanical molecular-orbital close-coupling (QMOCC) method over a wide energy range of 10-3 to 103 eV/u. Total and state-selective cross sections have been investigated and compared with the available theoretical and experimental data, and the state-selective rate coefficients for the temperature range of 100-10000 K have been obtained. In the present work, all the necessary highly excited state are included, and the influence of rotational couplings and 10 active electrons are considered. It is found that in the energy below 10 eV/u, the Na(4s) state is the most dominant exit state with a contribution of approximately 78% to the branch fraction, which is in best agreement with the experimental data. For energies above 10 eV/u, the MN total cross section is larger than those obtained in other theoretical calculations and shows a slow decreasing trend because the main exit states change, when the energy is above 100 eV/u, the dominant exit state becomes the Na(3p) state, while the Na(4s) state becomes the third most important exit state.

Electron excitation processes in low energy collisions of hydrogen–helium atoms

The electron excitation processes of H(1s) + He(1s2) → H(2s/2p) + He(1s2) are studied in impact energy range of 20--2000 eV/u by using the quantum-mechanical molecular orbital close-coupling (QMOCC) method. Total and state-selective cross sections have been obtained and compared with the available theoretical and experimental results. The results agree well with available measurements in the overlapping energy regions overall. The comparison of our results with other theoretical calculations further demonstrates the importance of considering a sufficient number of channels. The datasets presented in this paper, including the excitation cross sections, are openly available at https://www.doi.org/10.57760/sciencedb.j00113.00083.

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.

Measurements of charge transfer and target-electron-loss cross sections forH+,D+, andHe+impact on lithium at low energies

Experimental cross section measurements for charge transfer and for electron loss from lithium via charge transfer and direct ionization are reported for collisions between light ions and lithium atoms. Beams of protons, deuterium ions, and helium ions intersect a lithium atom beam, and collision cross sections are inferred by measuring the number of lithium ions produced in the collisions. The collision energy ranges studied are 0.13--3.5 keV for proton impact, 0.13--0.83 keV for deuterium ion impact, and 0.28--3 keV for helium ion impact. At proton collision energies below 0.7 keV our charge transfer cross sections are in excellent agreement with the theoretical predictions, resolving a long-standing discrepancy between theory and experiment in this energy range. Cross sections for proton and for deuterium ion impact on lithium are measured to be identical when scaled to the same collision velocity, indicating that quantum effects are not significant in the energy range studied. Comparison between our cross section measurements for lithium electron loss due to helium ion impact and previously measured charge transfer cross sections show that ionization is a negligible process in ${\mathrm{He}}^{+}+\mathrm{Li}$ collisions at energies below 3 keV. Undulations in the measured collision cross sections at low energy are observed for both proton and helium ion impact and are compared to molecular orbital close-coupling calculations.

Charge transfer and excitation processes in low energy collisions of He+ ions with Li atoms

Electron capture between solar wind ions and neutral species has contributed to the understanding of X-ray production from solar system bodies. The charge transfer and excitation processes in solar wind ions of He+(1s) colliding with Li(1s 22s) atoms are studied by utilizing the full quantum-mechanical molecular-orbital close-coupling (QMOCC) method with impact energies of 0.003–2 keV amu−1. Comparisons of cross sections from single- and multi-configurational calculations for a self-consistent field (SCF and MCSCF) process are carried out. Results show that the dominant reaction channels are He(1s2l 1,3L) + Li+(1s 2 1S). Good consistency is found among present total and state-selective charge transfer and excitation cross sections with other theoretical and experimental data in the same energy region. Due to the differences between coupling matrix elements in high-energy states, the charge transfer cross sections calculated from SCF and MCSCF split slightly as E > 0.4 keV amu−1. Weak Stueckelberg oscillations for charge transfer appear in the present work. In addition, the differences of cross sections for electron excitation to Li(1s 22p) in the singlet/triplet molecular states with He+(1s) are much smaller than those of charge transfer processes because of the similar energy gaps from Li(1s 22p) to the ground state in singlet/triplet states in the large R region.

Charge transfer in low-energy collisions of Be3+ and B4+ ions with He**Project supported by the National Natural Science Foundation of China (Grant Nos. 11774344, 11474033, and 11574326) and the National Key Research and Development Program of China (Grant No. 2017YFA0402300).

The nonradiative charge-transfer processes of Be3+(1s)/B4+(1s) colliding with He(1s2) are investigated by the quantum-mechanical molecular orbital close-coupling (QMOCC) method from 10 eV/u to 1800 eV/u. Total and state-selective cross sections are obtained and compared with other results available. Although the incident ions have the same number of electrons and collide with the same target, their cross sections are different due to the differences in molecular structure. For Be3+(1s) + He(1s2), only single-electron-capture (SEC) states are important and the total cross sections have a broad maximum around E = 150 eV/u. While for B4+(1s) + He(1s2), both the SEC and double-electron-capture (DEC) processes are important, and the total SEC and DEC cross sections decrease rapidly with the energy decreasing.

The Rb + –Rb collision rate in the energy range of 103–104 K

We study both theoretically and experimentally the energy dependence of the low-energy Rb+–Rb total collision rate k ia in the energy range from 103 to 104 K. We calculate the integral elastic cross-section and the resonant charge-transfer cross-section by the quantum mechanical molecular orbital close-coupling method, and then obtain k ia for temperatures by averaging the cross-sections over a Maxwell–Boltzmann velocity distribution. The experiments are conducted in an ion–neutral hybrid trap, where the Rb+ ions are created by photo-ionization of the cold atoms in a magneto-optic trap (MOT) and accumulated in the linear Paul ion trap. The total ion–atom collision rate k ia is measured by monitoring the fluorescence reduction of the steady-state MOT atoms by sequentially introducing photo-ionization and ion–atom collisions. The ion–atom collision energy E col ≈ T i is modified by changing T i due to T i being more than six orders of magnitude larger than the T a of cold atoms. The temperature of ions T i is obtained by comparing the time-of-flight mass spectrometry of Rb+ from experimental results to that obtained by SIMION simulation. The equilibrium steady T i is modified by changing the initial root-mean-squared position of the ion cloud, and the k ia are measured with E col from 8000 to 16 000 K. Both the theoretical and experimental results show that k ia increases with E col. More specifically, the measured k ia increases rapidly with the enlargement of E col near 10 000 K. The theoretical calculation results show that k ia increases slowly with E col. The specific difference may be due to the influence of the ratio of excited states f e on the trend of k ia at different E col.

Single- and Double-Electron Capture Processes in Low-Energy Collisions of N4+ Ions with He**Supported by the National Natural Science Foundation of China under Grant Nos. 11774344, 11474033 and 11574326, and the National Key Research and Development Program of China under Grant No. 2017YFA0402300.

We investigate the electron capture processes of N4+(1s22s) colliding with He(1s2) in the energy range of 10–1700 eV/amu using the quantum-mechanical molecular-orbital close-coupling (QMOCC) method. Total and state-selective single-electron capture and double-electron capture (SEC and DEC) cross sections are obtained and compared with other available studies. The results agree better with the experimental data in both trend and magnitude when the electron translation factor (ETF) effects are included. Our results indicate that both the SEC and DEC processes play important roles in the considered energy region. For the SEC processes, the N3+(1s22p2) + He+(1s) states are the dominant capture states, and the N2+(1s22s2p2) + He2+ states are the main DEC states.

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.

Theoretical study of resonances formed in low-energy Li− + H collisions

The full quantum molecular orbital close-coupling (QMOCC) method and optical potential method have been employed to study the nonradiative charge transfer and radiative decay processes for Li− colliding with H atoms. The cross sections of these processes are calculated rigorously in the energy range of 0.1–1.2 eV. It is found that rich and significant resonance structures appear at the same positions in the cross sections for both nonradiative charge transfer and radiative decay processes. The primary resonances are identified and studied by QMOCC (by fitting the eigenphase sum of the K-matrix) and complex absorbing potential (CAP) method. The resonance parameters calculated by CAP agree very well with those extracted from QMOCC calculations.

Charge Exchange X-Ray Emission due to Highly Charged Ion Collisions with H, He, and H2: Line Ratios for Heliospheric and Interstellar Applications

Abstract The fundamental collisional process of charge exchange (CX) has been established as a primary source of X-ray emission from the heliosphere, planetary exospheres, and supernova remnants. In this process, X-ray emission results from the capture of an electron by a highly charged ion from a neutral atom or molecule, to form a highly excited, high-charge state ion. As the captured electron cascades down to the lowest energy level, photons are emitted, including X-rays. To provide reliable CX-induced X-ray spectral models to realistically simulate these environments, line ratios and spectra are computed using theoretical CX cross sections obtained with the multi-channel Landau-Zener, atomic-orbital close-coupling, molecular-orbital close-coupling, and classical trajectory Monte Carlo methods for various collisional velocities relevant to astrophysics. X-ray spectra were computed for collisions of bare and H-like C to Al ions with H, He, and H2 with results compared to available experimental data. Using these line ratios, XSPEC models of CX emission in the northeast rim of the Cygnus Loop supernova remnant and the heliosphere are shown as examples with ion velocity dependence.

Cross sections for state-selective electron capture and excitation in He+–H collisions

Electron-capture and excitation processes in He+ +H collisions have been studied by using the full quantum-mechanical molecular orbital close-coupling (QMOCC) and the two-center atomic orbital close-coupling (TC-AOCC) methods in the energy ranges 10-2–5 keV/u and 0.1–100 keV/u, respectively. The spin-selected state-selective cross sections for these processes in the He+ +H collision system are reported for the first time. The spin-averaged total electron capture and excitation cross sections, as well as the emission cross section for Balmer α radiation, are compared with the results of available experimental and previous theoretical results in the overlapping energy ranges.

Ab initio study of charge transfer in low energy collisions of B4+ with H

The charge transfer processes in collisions of B4+(1s) ions with H(1s) atoms are investigated by using the quantum-mechanical molecular orbital close-coupling method with electron translational effects included in the impact energy region of 10-5 − 20 keV/u. Molecular data with high accuracy are calculated using ab initio method. Our calculations clarified the controversy in the total and state-selective cross sections at low energies. The treatment of the core electron will influence the accuracy of the calculated molecular structure and then sensitively influence the charge transfer cross sections in the low energy region. The rotational couplings play an important role in the state-selective cross sections at energies above 50 eV/u, but weakly influence the total cross sections for this collision system.

Spin-resolved state-selective electron capture in C5+-H collisions

The electron capture processes in the C5+(1s)+H(1s) collision system are investigated by the quantum-mechanical molecular orbital close-coupling (QMOCC) method in the energy range of 10−5–10 keV u−1. Accurate molecular structure calculations are performed by the ab initio multireference single- and double-excitation configuration interaction method. The electron translational effects are included in the calculations. The total and spin-resolved state-selective cross sections are presented and compared with the available experimental and theoretical data. The present results have a good agreement with the experimental measurements. Our calculations show that the electron translation factors play a very important role for energies above 0.1 keV u−1 leading to significant differences between the present and the previous QMOOC cross section results of Nolte et al 2012 (J. Phys. B: At. Mol. Opt. Phys. 45 245202). The effects of the core electron also cannot be ignored below 2 keV u−1. Model potential calculations, in which the core electron is treated as frozen, cannot give accurate spin-resolved cross sections.

Theoretical investigation of electron transfer and detachment processes in low energy H− + Li and Li− + H collisions

The charge exchange and collisional detachment processes in H− + Li and Li− + H collisions have been studied by using the quantal molecular orbital close-coupling (QMOCC) method in the energy ranges of about 0.12–1000 eV u−1 and 0.1 meV–1000 eV, respectively, and the inelastic collision cross sections and rate coefficients have been computed and presented. It is found that the electron transfer process in the H− + Li and Li− + H collisions is due to the Demkov coupling between the 12Σ+ and 22Σ+ states at internuclear distances of about 15a0. The collisional electron detachment in the considered collision system is due to the excitation of the remaining six states, which are all unstable against autodetachment. These states are populated through a series of Landau–Zener couplings of the 22Σ+ state with upper 2Σ+ states and by the rotational 2Σ+–2Π couplings at small internuclear distances. The cross sections for electron transfer in H− + Li and Li− + H collisions in the energy range of 10–1000 eV u−1 attain values in the range of 10−16–10−15 cm2 (reaching their maximum values of about 5 × 10−15 cm2 at 500–600 eV u−1), while the values of the corresponding electron detachment cross sections in this energy range attain generally smaller values.

Resonant charge transfer in slow Li+−Li(2s) collisions**Project supported by the National Natural Science Foundation of China (Grant Nos. 11179041, 11474032, and 11474033) and the NSAF (Grant No. U1330117).

The resonant charge transfer process for Li+−Li(2s) collision is investigated by the quantum-mechanical molecular orbital close-coupling (QMOCC) method and the two-center atomic-orbital close-coupling (AOCC) method in an energy range of 1.0 eV/u–104 eV/u. Accurate molecular structure data and charge transfer cross sections are given. Both the all-electron model (AEM) and one-electron model (OEM) are used in the QMOCC calculations, and the discrepancies between the two models are analyzed. The OEM calculation can also give a reliable prediction of the cross sections for energies below 1 keV/u.

Charge transfer in collisions of Beq+ (q=2-4) and Bq+ (q=3-5) ions with H

The charge transfer reactions in collisions of Beq+(q=2-3) and Bq+(q=3-4) ions and atomic hydrogen are investigated by using the quantal molecular orbital close-coupling (QMOCC) and the two-center atomic-orbital close-coupling (TC-AOCC) methods. Total and sub-shells state-selective cross sections are calculated for low and intermediate energy region and compared with other data available. Sets of recommended cross sections, based on the QMOCC and TC-AOCC calculations, are deduced and tabulated for Be2,3+ + H and B3,4+ + H collisions, which provide important atomic data needed in the charge-exchange-recombination spectroscopy diagnostics in magnetic fusion plasmas investigation.