Two-center Atomic Orbital Close-coupling Research Articles

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.

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.

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.

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.

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.

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.

Total, state-selective and differential cross sections for single electron capture in He+–He collisions

The total, state-selective and angular-differential cross sections for single electron capture in He+–He collisions are investigated by using the two-center atomic orbital close-coupling method in the energy range 0.2–650 keV/u. The angular-differential cross sections for electron capture to the ground state of He are calculated at collision energies of 0.625, 1.25, 7.5, 25, 60, and 150 keV/u within the eikonal approximation for the scattering amplitude. Both total and differential cross sections are compared with the available experimental and theoretical data. The calculated differential cross sections exhibit oscillatory structures with exponentially decreasing amplitude and frequency decreasing with increasing the collision energy. They show good agreement with the experimental data for scattering angles where decreases with increasing the collision energy ( for E = 0.625 keV/u, for E = 150 keV/u). We found out that for a given collision energy, the oscillatory structure of angular-differential cross section is strongly correlated with the oscillatory structure of the impact parameter dependence of electron capture probability.

Electron capture and excitation processes in collisions of H+ with H in finite-temperature quantum plasmas

Electron capture and excitation processes in H+-H collisions imbedded in warm dense quantum plasmas are studied by the two-center atomic orbital close-coupling (TC-AOCC) method in the energy range 1–200 keV. The screened potential which is used to describe the interaction between charged particles incorporates the quantum electron degeneracy, exchange-correlation and finite-temperature gradient correlation effects. The total and state-selective electron capture and excitation cross-sections for this collision system with this potential are calculated in a wide range of plasma densities and temperatures. It is demonstrated that the screening of Coulomb interactions affects the collision dynamics and the magnitude and energy behavior of the excitation and electron capture cross-sections. The results at very low and high temperatures are also compared with those obtained for zero-temperature quantum plasmas and Debye plasmas, respectively.

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.

Solar wind charge exchange in laboratory – Observation of forbidden X-ray transitions

We have reproduced solar wind charge exchange collisions of hydrogen-like O7+ ions with He gas at collision energies of 42keV in the laboratory and observed the forbidden transition of 1s21S0–1s2s 3S1 in helium-like O6+ ions produced by single electron capture. The measured soft X-ray spectrum had a peak at 560eV which corresponds to the energy of the forbidden 1s21S0–1s2s 3S1 transition in the O6+ ion, and a reasonable energy difference between peak positions of the forbidden and resonance lines was found, which ensured that we succeeded in observing the forbidden transition of O6+ ions. The dominant electron capture level in the collision of O7+ ions with He can be estimated to be a principal quantum number n=4 by the classical over barrier model and the two-center atomic orbital close coupling method. After the charge exchange, the population of the 1s2s state becomes large due to cascade transitions from the higher excited states, so the long-lived forbidden transition to the 1s21S0 ground state is one of main features observed in the charge exchange spectra.

Electron capture and excitation processes in H+−H collisions in dense quantum plasmas

Electron capture and excitation processes in proton–hydrogen atom collisions taking place in dense quantum plasmas are studied by employing the two-centre atomic orbital close-coupling (TC-AOCC) method. The Debye–Hückel cosine (DHC) potential is used to describe the plasma screening effects on the Coulomb interaction between charged particles. The properties of a hydrogen atom with DHC potential are investigated as a function of the screening strength of the potential. It is found that the decrease in binding energy of nl levels with increasing screening strength is considerably faster than in the case of the Debye–Hückel (DH) screening potential, appropriate for description of charged particle interactions in weakly coupled classical plasmas. This results in a reduction in the number of bound states in the DHC potential with respect to that in the DH potential for the same plasma screening strength, and is reflected in the dynamics of excitation and electron capture processes for the two screened potentials. The TC-AOCC cross sections for total and state-selective electron capture and excitation cross sections with the DHC potential are calculated for a number of representative screening strengths in the 1–300 keV energy range and compared with those for the DH and pure Coulomb potential. The total capture cross sections for a selected number of screening strengths are compared with the available results from classical trajectory Monte Carlo calculations.

Alignment of H(2p) in collisions of protons and antiprotons with hydrogen atoms with screened Coulomb interaction

The effects of screened Coulomb interaction on the alignment of H(2p) state produced in collisions of hydrogen atoms with protons and antiprotons are investigated in the energy range 1–200 keV by using the two-center atomic orbital close-coupling (TC-AOCC) method. It is shown that the decrease of the binding energy of hydrogen nl-states and the reduction of the number of bound states with increasing the strength of the screening affect significantly the alignment degree and its energy dependence. In the case of antiproton-H collision the difference between the alignments with screened and unscreened Coulomb potential increases with increasing the strength of the screening in the entire energy range above 2 keV/u, while in the case of proton-H collision it does so only in the energy range 5–25 keV/u.

Spin-resolved electron capture and excitation processes in He+-Li collisions

The electron capture and excitation processes in collisions of He+-Li are investigated theoretically by using the two-center atomic orbital close-coupling method in the energy range 0.1–100 keV u−1. The interaction of active electrons with the projectile ion is represented by a model potential different for the singlet and triplet systems of He states. The spin-averaged electron capture cross section of present calculations is compared with the available experimental data and with the results of other theoretical calculations and good agreement is obtained in the overlapping energy range. It is found that the cross sections for electron capture to singlet and triplet states of He are significantly different for energies below 5 keV u−1. However, the spin-resolved He+-Li interactions do not affect the excitation cross sections considerably.

Dynamics of N5+-H electron capture in Debye plasmas

The electron capture in N5+-H collisions imbedded in a Debye plasma is studied by using the two-center atomic orbital close-coupling method in the energy range from 1 keV/u to 200 keV/u. The atomic orbitals and electron binding energies of atomic states are calculated within the Debye–Hückel approximation of the screened Coulomb potential and used in atomic orbital close-coupling dynamics formalism to calculate the electron capture cross sections. The electron capture cross sections and the charge transfer spectral lines of N4+(1s2nl) for a number of representative screening parameter values are presented and discussed. It is found that the screening of Coulomb interactions affects the entire collision dynamics and the magnitude and energy behavior of state-selective cross sections. The changes in electron binding energies and capture cross sections when the interaction screening varies introduce dramatic changes in the radiation spectrum of N4+(1s2nl) capture states with respect to the unscreened interaction case.

Polarization of Balmer alpha radiation resulting from H++H collisions in Debye plasmas

The linear polarization degree of Balmer alpha radiation resulting from H++H(1s) collisions in a hot, dense weakly coupled plasma is studied in the energy range 1–140 keV/u by adopting the Debye-Hückel potential to represent the screened interaction between charged plasma particles. Due to the energy splitting of nl hydrogen states in the short range Debye-Huckel potential, the Balmer alpha radiation contains three components corresponding to 3s-2p, 3p-2s, and 3d-2p transitions, of which only the last two can be linearly polarized. For calculation of 3lm excitation and electron capture cross sections, the two-center expansion atomic orbital close coupling method is used for a number of Debye screening lengths. The effects of plasma screening on the 3lm cross sections are manifested in significant changes of their magnitudes and energy behavior with respect to the ones in the unscreened case, producing significant changes in the polarization degree of Balmer 3p-2s and 3d-2p lines.

Spin-resolved electron capture cross sections for C5+-H collisions

The charge transfer process in C5+-H collisions has been theoretically studied using the two-center atomic orbital close-coupling method in the energy interval from 0.1 to 300 keV u−1. The interaction of active electron with the projectile ion is represented by model potentials different for the singlet and triplet systems of C4+(1snl) states. The results of the present calculations are compared with other theoretical results and experimental measurements and good agreement is obtained for the total spin-averaged cross sections in the overlapping energy range. For the spin-resolved cross sections, we found that the present total and n-shell electron capture cross sections are also in good agreement with the results of other theoretical studies in the overlapping energy range for both the singlet and triplet cases. Good overall agreement has been obtained with the results of other authors for the nl-state-selective cross sections, except for the capture to 3p and 4p singlet states at the low collision energies.

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.

Polarization of Li(nd → 2p, n = 3–5) emission resulting from He2+–Li collisions

The excitation of a ground state Li atom to its 1s2nd (n = 3–5) excited states in a collision with He2+ is investigated using the two-center atomic orbital close-coupling method. The Li(nd → 2p) emission cross-sections are calculated in the collision energy range of 1–150 keV u−1 and compared with the available experimental cross-sections and other theoretical results in the overlapping energy range, showing good overall agreement. The linear polarization degrees of the radiation from the nd 2D3/2–2p 2P1/2, nd 2D3/2–2p 2P3/2 and nd 2D5/2–2p 2P3/2 (n = 3–5) transitions in Li are also calculated from the ndm magnetic substate populations. It is found that polarization degrees for nd → 2p (n = 3–5) transitions exhibit sharp minima at ∼3 keV u−1 which originate from the peaks in the Li(nd → 2p) (n = 3–5) emission cross-sections at about the same energy.