Convergent Close-coupling Calculations Research Articles

Calculations of positron scattering from F, F2, HF, and various fluorocarbons

Abstract Single center convergent close-coupling (CCC) calculations have been completed for positron scattering from atomic fluorine. Total, electron-loss, positronium-formation, direct ionization, momentum transfer, elastic, bound-state excitation, and stopping power cross sections have been determined for energies between threshold and 5000 eV. Past calculations for this scattering system exist only for elastic and momentum-transfer cross sections. For high energies, good agreement is found between current and past results. At low energies, however, large differences are found between the current calculations and previous results. The atomic fluorine results are then used in a modified independent atom approach to calculate cross sections for positron scattering on F2, HF, CF4, C2F6, C3F6, C3F8, and C6F6. The current molecular results are typically higher than previous positron experiments across the calculated energy range, however, these experiments were not corrected for the forward angle scattering effect and likely underestimate the true result. Good agreement is found between the current positron results and previous electron experiments and calculations at high energies.

Calculations of Positron Scattering from Boron, BH, BF, BF2, and BF3

The single-center convergent close-coupling (CCC) method is applied to calculate positron scattering from boron. A model potential approach is utilized to extract the positronium formation, direct ionization, and values between the positronium formation and ionization thresholds. We present results for total, electron loss, elastic, momentum transfer, total bound state excitation, positronium formation, direct ionization, stopping power, and mean excitation energy from 10−5 eV to 5000 eV. For boron, there is only one other set of theoretical positron calculations for elastic and momentum transfer above 500 eV, which is in excellent agreement with the current CCC results. Using the current results for boron atoms and previous CCC calculations for hydrogen and fluorine atoms, positron scattering from BF, BF2, BF3, and BH molecules is calculated for energies between 0.1 eV and 5000 eV with a modified independent atom approach.

Elastic Electron Scattering from Be, Mg, and Ca

We present a comprehensive set of theoretical results for differential, integrated, and momentum transfer cross sections for the elastic scattering of electrons by beryllium, magnesium, and calcium at energies below 1 keV. In addition, we provide Sherman function values for elastic electron scattering from calcium in the same energy range. This study extends the application of our method of calculations, already employed for barium and strontium, to all stable alkaline-earth-metal atoms. Our semi-empirical approach to treating target polarization has produced in our earlier work a satisfactory agreement with experimental values and precise theoretical results such as convergent close-coupling calculations for barium. The present data are expected to be of similar high accuracy, based on our previous success in similar calculations for barium and all inert gases.

Calculations of positron scattering from small molecules

Recently, convergent close-coupling calculations have been completed for positron scattering from the carbon and oxygen atomic targets. These, together with previously completed calculations for atomic hydrogen, are utilized to perform positron scattering calculations for molecular hydrogen (H2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {H}_2$$\\end{document}), molecular oxygen (O2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {O}_2$$\\end{document}), diatomic carbon (C2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {C}_2$$\\end{document}), carbon monoxide (CO), carbon dioxide (CO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {CO}_2$$\\end{document}), ozone (O3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {O}_3$$\\end{document}), water (H2O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {H}_2\\hbox {O}$$\\end{document}), and methane (CH4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {CH}_4$$\\end{document}) through a modified independent atom approach. For these molecules, positronium-formation, direct ionization, electron-loss, elastic, total electronic excitation, total inelastic, and total cross sections are obtained for energies between 0.1 and 5000 eV. There is, in general, good agreement between the current results and past experiments for most transitions, particularly at high energies where this approach is expected to be most accurate.Graphic

Convergent close-coupling calculations of positron scattering from neon and argon

Positron scattering from the noble gas atoms neon and argon is calculated using the single-center convergent close-coupling (CCC) method. Unlike previous CCC calculations, we have relaxed the frozen-core approximation by fully opening the outermost s and p shells, and find better agreement with experiment for excitation energies and dipole polarizability. We have used this improved structure model to calculate elastic, elastic differential, total, momentum-transfer, electron-loss, and total bound excitation cross sections. We have applied a complex model potential calculation, scaled to our single-center CCC results, to obtain direct ionization and positronium-formation cross sections for these systems. This complex model potential was also used to calculate results between the positronium-formation and ionization thresholds, giving complete results from 10-5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-5}$$\\end{document} eV to 5000 eV. Overall, good agreement is observed with past theory and experiment for most transitions.Graphic abstract

Antiproton collisions with excited positronium

We present results of calculations of several processes resulting from positronium (Ps) collisions with antiprotons: antihydrogen formation, Ps breakup, and ${n}_{\mathrm{Ps}}$-changing collisions. Calculations utilize the quantum convergent close-coupling (CCC) method and the classical trajectory Monte Carlo (CTMC) method. We identify a region of Ps principal quantum numbers ${n}_{\mathrm{Ps}}$ and Ps energies where the classical description is valid and where the CCC calculations become computationally too expensive. This allows us to present the most complete and reliable set of cross sections in a broad range of ${n}_{\mathrm{Ps}}$ and initial orbital momentum quantum numbers ${l}_{\mathrm{Ps}}$ which are necessary for experiments with antihydrogen at CERN.

Modeling the Mg I from the NUV to MIR

Context. Semi-empirical models of the solar atmosphere are used to study the radiative environment of any planet in our Solar System. There is a need for reliable atomic data for neutral atoms and ions in the atmosphere to obtain improved calculated spectra. Atomic parameters are crucial to computing the correct population of elements through the whole stellar atmosphere. Although there is very good agreement between the observed and calculated spectra for the Sun, there is still a mismatch in several spectral ranges due to the lack of atomic data and the inaccuracies thereof, particularly for neutrals such as Mg I. Aims. To represent many spectral lines of Mg I from the near-ultraviolet to the mid-infrared correctly, it is necessary to add and update the atomic data involved in the atomic processes that drive their formation. Methods. The improvements made to the Mg I atomic model are as follows: i) 127 strong lines, including their broadening data, were added. ii) To obtain these new lines, we increased the number of energy levels from 26 to 85. iii) Photoionization cross-section parameters were added and updated. iv) Effective collision strength (ϒij) parameters were updated for the first 25 levels using the existing data from the convergent close-coupling calculations. One of the most significant changes in our model is given by the new ϒij parameters for transitions involving levels between 26 and 54, which were computed with a multiconfiguration Breit–Pauli distorted-wave (DW) method. For transitions involving superlevels, we calculated the ϒij parameters with the usual semi-empirical formulas. Results. More than 100 transitions were added to our calculations, increasing our capability of reproducing important features observed in the solar spectra. We found a remarkable improvement in matching the solar spectra for wavelengths higher than 30 000 Å when our new DW ϒij data were used in the model.

Extraction of Ps-formation cross-sections from single-centre positron-scattering calculations

Positron scattering on atomic and molecular targets is a two-centre problem due to the possibility of rearrangement (Ps-formation) processes. In certain kinematic regions, single-centre expansion methods can be applied to two-centre scattering problems. In such approaches, however, information about Ps-formation and direct ionization processes are combined into excitation amplitudes of positive-energy pseudostates. In this report we show that Ps-formation amplitudes can be extracted using the total scattering wave function, which we reconstruct from single-centre convergent close-coupling calculations. The method is applied to positron scattering from hydrogen and lithium atomic targets. Excellent agreement with the two-centre theoretical benchmark results show the validity of the proposed technique.

Convergent close-coupling calculations of electrons scattering on electronically excited molecular hydrogen

We use the adiabatic-nuclei molecular convergent close-coupling method to perform calculations of 0.01--1000 eV electrons scattering on the $c^{3}\mathrm{\ensuremath{\Pi}}_{u}$, $a^{3}\mathrm{\ensuremath{\Sigma}}_{g}^{+}$, $B^{1}\mathrm{\ensuremath{\Sigma}}_{u}^{+}$, $C^{1}\mathrm{\ensuremath{\Pi}}_{u}$, and $EF^{1}\mathrm{\ensuremath{\Sigma}}_{g}^{+}$ states of ${\mathrm{H}}_{2}$ in the $v=0$ vibrational level. Elastic, superelastic, ionization, and grand-total cross sections are presented, as well as cross sections for excitation of the $n=2$--3 singlet and triplet states of ${\mathrm{H}}_{2}$ (where $n$ is the atomic-limit principle quantum number). Comparison with available theoretical results is made. Good agreement is found with the recent $R$-matrix results [J. Phys. B 53, 245203 (2020)] for most of the exchange and dipole-forbidden transitions, but not for the dipole-allowed transitions. The sources of disagreement were found to be an unconverged partial-wave expansion and the utilization of the fixed-nuclei approximation (as opposed to adiabatic-nuclei) in the $R$-matrix calculations.

Isotopic and vibrational-level dependence of H2 dissociation by electron impact

The low-energy electron-impact dissociation of molecular hydrogen has been a source of disagreement between various calculations and measurements for decades. Excitation of the ground state of H$_2$ into the dissociative $b ^3\Sigma_u^+$ state is now well understood, with the most recent measurements being in excellent agreement with the molecular convergent close-coupling (MCCC) calculations of both integral and differential cross sections (2018 Phys. Rev. A 98 062704). However, in the absence of similar measurements for vibrationally-excited or isotopically-substituted H$_2$, cross sections for dissociation of these species must be determined by theory alone. We have identified large discrepancies between MCCC calculations and the recommended $R$-matrix cross sections for dissociation of vibrationally-excited H$_2$, D$_2$, T$_2$, HD, HT, and DT (2002 Plasma Phys. Contr. F. 44 1263-1276,2217-2230), with disagreement in both the isotope effect and dependence on initial vibrational level. Here we investigate the source of the discrepancies, and discuss the consequences for plasma models which have incorporated the previously recommended data.

Convergent close-coupling calculations of positron collisions with the hydrogen negative ion

SynopsisConvergent close-coupling method has been applied to positron scattering by the hydrogen negative ion. Internal consistency of the method and convergence of the cross sections are achieved with use of both the single- and two-centre approaches. Calculations were performed using accurate target wave functions obtained with the multi-core approach.

Electron-Impact Dissociation of Vibrationally-Excited Molecular Hydrogen into Neutral Fragments

We present convergent close-coupling (CCC) calculations of electron-impact dissociation of vibrationally-excited molecular hydrogen into neutral fragments. This work follows from our previous results for dissociation of molecular hydrogen in the ground vibrational level [Scarlett et al., Eur. Phys. J. D 72, 34 (2018)], which were obtained from calculations performed in a spherical coordinate system. The present calculations, performed utilizing a spheroidal formulation of the molecular CCC method, reproduce the previous dissociation cross sections for the ground vibrational level, while allowing the extension to scattering on excited levels.

Low-energy electron scattering from molecular hydrogen: Excitation of the X1Σg+ to b3Σu+ transition

We present time-of-flight differential cross-section measurements and convergent close-coupling calculations of differential cross sections for the electron-impact excitation of the $X\phantom{\rule{0.16em}{0ex}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}\ensuremath{\rightarrow}b\phantom{\rule{0.16em}{0ex}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$ transition in molecular hydrogen. A part of this work was recently published [M. Zawadzki et al., Phys. Rev. A 97, 050702(R) (2018)]. In this work, agreement between theory and experiment is excellent overall, and marks a transition in electron-molecule scattering where differential scattering of excitation is found to be in such precise agreement. We also present total electron-impact excitation differential cross sections for ${\mathrm{H}}_{2}$ for which agreement between theory and experiment is found to be excellent.

Time-of-flight electron scattering from molecular hydrogen: Benchmark cross sections for excitation of the X1Σg+→b3Σu+ transition

The electron impact $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}\ensuremath{\rightarrow}b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$ transition in molecular hydrogen is one of the most important dissociation pathways to forming atomic hydrogen atoms, and is of great importance in modeling astrophysical and industrial plasmas where molecular hydrogen is a substantial constituent. Recently, it has been found that the convergent close-coupling (CCC) cross sections of Zammit et al. [Phys. Rev. A 95, 022708 (2017)] are up to a factor of 2 smaller than the currently recommended data. We have determined normalized differential cross sections for excitation of this transition from our experimental ratios of the inelastic to elastic scattering of electrons by molecular hydrogen using a transmission-free time-of-flight electron spectrometer, and find excellent agreement with the CCC calculations. Since there is already excellent agreement for the absolute elastic differential cross sections, we establish benchmark differential and integrated cross sections for the $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}\ensuremath{\rightarrow}b{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$ transition, with theory and experiment being essentially in complete agreement.

Electron-impact dissociation of molecular hydrogen into neutral fragments

We present convergent close-coupling calculations of electron-impact dissociation of the ground state of molecular hydrogen into neutral fragments over the range of impact energies from 6 to 300 eV. The calculations account for dissociative excitation, excitation radiative decay dissociation, and predissociation through all bound electronic triplet states, and singlet states up to the state. An estimate is given for the contribution from the remaining bound electronic singlet states. Our results are in agreement with the recommended data of Yoon et al. [J. Phys. Chem. Ref. Data 37 , 913 (2008)] in the low (6–12 eV) and high (60–70 eV) energy regions, but somewhat lower at the intermediate energies.

Low-energy l-mixing collisions of excited positronium with protons and antiprotons

We investigate l-mixing processes in collisions of excited positronium (Ps) atoms with protons in the range of the principal quantum number n of the Ps atom between 4 and 8. We show first that results of the threshold theory agree very well with convergent close-coupling calculations. We then compare quantum cross sections with results of semiclassical and classical theories. In the semiclassical theory, the Ps atom is treated quantum-mechanically, whereas the relative Ps-p motion is described classically. For l-mixing processes there is a good agreement between quantum and semiclassical results, whereas classical theory strongly underestimates the l-mixing cross sections. The conclusions are important for the interpretation of Classical Trajectory Monte Carlo simulations and the use of their data in the design of experiments.

Electron collisions with beryllium and its ions

An overview is provided of the convergent close-coupling calculations for electron- impact on neutral beryllium, as well as its various ionic stages. The calculations were performed from near threshold to high energies with initial states having principal quantum number n ≤ 4. Excitation to states with n ≤ 5 and total ionisation cross sections have been calculated with an estimated accuracy of below 10% at all energies considered.

Discrepancy between theory and experiment in double ionization of helium by fast electrons

We compute fully differential cross sections for double ionization of helium by electrons, within the high-impact-energy and low-momentum transfer regimes, using the generalized Sturmian functions approach. Our results are converged relative to the total angular momentum and variable domain size. The method shows very good agreement with convergent close coupling calculations performed by Kheifets et al. [J. Phys. B 32, 5047 (1999)] for all ejection angles for the two electron emission energies considered in the experiments reported in that contribution. Both theoretical methods provide fully differential cross sections that require the same upscaling factors to compare with experimental data and are based on a first-order Born model for the projectile-target interaction. Since that reference was published, there were several theoretical efforts to account for the absolute scale of the experimental results, but agreement in the cross-section magnitude was not achieved even between theories. With the present contribution we conclude that the first-order Born model is now adequately solved, shifting the magnitude controversy towards either the experimental data and/or the addition of higher degrees of projectile-target interaction to the calculation.

Differential cross section for the double photoionization of Mg

The time-dependent close-coupling (TDCC) method is used to calculate the energy and angle triple differential cross section for the double photoionization of Mg() at a photon energy of 55.49 eV to compare with recent converged close-coupling (CCC) calculations and in support of recent experiments at ELETTRA. Comparisons are made between the TDCC, CCC, and experimental results for equal energy sharing at scattering angles of , , and , and for unequal energy sharing at and . Comparisons are made between the TDCC and CCC results for equal and unequal energy sharing at . In addition, TDCC, CCC, and experimental results are compared for complex scattering amplitudes and the TDCC method is used to calculate single energy differential cross sections at photon energies of 30, 35, 40, 45, and 55.49 eV. Although there are scattering angles in the triple differential cross sections at 55.49 eV at which the TDCC, CCC, and experimental results are quite different, the overall agreement between the theories and experiment is reasonable for such small cross sections.

Positron scattering and annihilation on noble-gas atoms

Positron scattering and annihilation on noble gas atoms below the positronium formation threshold is studied ab initio using many-body theory methods. The many-body theory provides a near-complete understanding of the positron-noble-gas-atom system at these energies and yields accurate numerical results. It accounts for positron-atom and electron-positron correlations, e.g., polarization of the atom by the incident positron and the non-perturbative process of virtual positronium formation. These correlations have a large effect on the scattering dynamics and result in a strong enhancement of the annihilation rates compared to the independent-particle mean-field description. Computed elastic scattering cross sections are found to be in good agreement with recent experimental results and Kohn variational and convergent close-coupling calculations. The calculated values of the annihilation rate parameter $Z_{\rm eff}$ (effective number of electrons participating in annihilation) rise steeply along the sequence of noble gas atoms due to the increasing strength of the correlation effects, and agree well with experimental data.