Convergent close-coupling calculations of electron-hydrogen scattering

Triply differential cross sections for electron and positron impact on methane

We here report theoretical triply differential cross sections (TDCS) for 250 eV electron and positron impact ionization of the methane molecule calculated within the second-order distorted-wave Born approximation (DWBA2) for various momentum transfer conditions. The experimental data taken from Işık et al. [J. Phys. B: At., Mol. Opt. Phys. 49, 065203 (2016)] will be compared with the current theoretical predictions as well as molecular three body distorted wave (M3DW) approximation and generalized Sturmian function (GSF) theoretical models in a non-coplanar geometry. In the low analyzer scattering plane, the results obtained within the DWBA2 theory show better agreement with the experimental results compared to the GSF results. The M3DW results also exhibit agreement with the experimental results, in particular in the perpendicular plane geometry. Furthermore, significant differences between electron and positron TDCS were observed.

Taking the Convergent Close-Coupling Method beyond Helium: The Utility of the Hartree-Fock Theory

The convergent close-coupling (CCC) method was initially developed to describe electron scattering on atomic hydrogen and the hydrogenic ions such as He+. The latter allows implementation of double photoionization (DPI) of the helium atom. For more complex single valence-electron atomic and ionic targets, the direct and exchange interaction with the inner electron core needs to be taken into account. For this purpose, the Hartree-Fock (HF) computer codes developed in the group of Miron Amusia have been adapted. In this brief review article, we demonstrate the utility of the HF technique by examples of electron scattering on Li and the DPI of the H− and Li− ions. We also discuss that modern-day computer infrastructure allows the associated CCC code, and others, to be readily run directly via the Atomic, Molecular and Optical Science Gateway.

Excitations of the nS States of Atomic Hydrogen by Electron Impact, Excitation Rate Coefficients, and Phase Shifts: Comparison with Positron Impact Excitation

The excitation cross-sections of the nS states of atomic hydrogen, n = 2 to 6, by electron impact on the ground state of atomic hydrogen were calculated using the variational polarized-orbital method at various incident electron energies in the range 10 to 122 eV. Converged excitation cross-sections were obtained using sixteen partial waves (L = 0 to 15). Excitation cross-sections to 2S state, calculated earlier, were calculated at higher energies than before. Results obtained using the hybrid theory (variational polarized orbital method) are compared to those obtained using other approaches such as the Born–Oppenheimer, close-coupling, R-matrix, and complex-exterior scaling methods using only the spherical symmetric wave functions. Phase shifts and elastic cross-sections are given at various energies and angular momenta. Excitation rate coefficients were calculated at various electron temperatures, which are required for plasma diagnostics in solar and astrophysics to infer plasma parameters. Excitation cross-sections are compared with those obtained by positron impact excitation.

All-Order Full-Coulomb Quantum Spectral Line-Shape Calculations

Understanding how atoms interact with hot dense matter is essential for astrophysical and laboratory plasmas. Interactions in high-density plasmas broaden spectral lines, providing a rare window into interactions that govern, for example, radiation transport in stars. However, up to now, spectral line-shape theories employed at least one of three common approximations: second-order Taylor treatment of broadening operator, dipole-only interactions between atom and plasma, and classical treatment of perturbing electrons. In this Letter, we remove all three approximations simultaneously for the first time and test the importance for two applications: neutral hydrogen and highly ionized magnesium and oxygen. We found 15%-50% change in the spectral line widths, which are sufficient to impact applications including white-dwarf mass determination, stellar-opacity research, and laboratory plasma diagnostics.

Electronic and Vibrational Close-Coupling Method for Resonant Electron-Molecule Scattering

We report the development of a vibrational-electronic convergent close-coupling method for electron-molecule scattering with an ab-initio account of the coupling between the electronic and vibrational motions. The technique has been applied to scattering on molecular hydrogen, including coupling between vibrational levels in the first 11 electronic states. Distinct resonances associated with the temporary formation of the H_{2}^{-} ion are present between 10 and 14 eV for numerous transitions, including vibrational excitation of the X ^{1}Σ_{g}^{+} state, dissociation via the b ^{3}Σ_{u}^{+} state, and excitation of the B ^{1}Σ_{u}^{+} state. With both resonant and nonresonant scattering treated in a single calculation, this method is capable of providing self-consistent sets of cross sections for electron-molecule scattering in regions where the adiabatic-nuclei approximation breaks down.

Benchmark Angle-Differential Cross-Section Ratios for Excitation of the 4p5s Configuration in Krypton

Benchmark intensity ratio measurements of the energy loss lines of krypton for excitation of the 4p61S0→4p55s[3/2]2, 4p55s[3/2]1, 4p55s′[1/2]0, and 4p55s′[1/2]1 transitions are reported, these being the lowest electronic excitations for krypton. The importance of these ratios as stringent tests of theoretical electron scattering models for the noble gases is discussed, as well as the role of spin-exchange and direct processes regarding the angular dependence of these ratios. The experimental data are compared with predictions from fully-relativistic B-spline R-matrix (close-coupling) calculations.

Capturing Correlation Effects on Photoionization Dynamics

A highly correlated combination of the equation-of-motion coupled cluster (EOM-CC) Dyson orbital and the multicentric B-spline time-dependent density functional theory (TDDFT)-based approach is proposed and implemented within the single-channel approximation to describe molecular photoionization processes. The twofold objective of the approach is to capture interchannel coupling effects, missing in the B-spline DFT treatment, and to explore the response of Dyson orbitals to strong correlation effects and its influence on the photoionization observables. We validate our scheme by computing partial cross sections, branching ratios, asymmetry parameters, and molecular frame photoelectron angular distributions of simple molecules. Finally, the method has been applied to the study of photoelectron spectra of the Ni(C₃H₅)₂ molecule, where giant correlation effects completely destroy the Koopmans picture.

Data Needs for Modeling Low-Temperature Non-Equilibrium Plasmas: The LXCat Project, History, Perspectives and a Tutorial

Technologies based on non-equilibrium, low-temperature plasmas are ubiquitous in today’s society. Plasma modeling plays an essential role in their understanding, development and optimization. An accurate description of electron and ion collisions with neutrals and their transport is required to correctly describe plasma properties as a function of external parameters. LXCat is an open-access, web-based platform for storing, exchanging and manipulating data needed for modeling the electron and ion components of non-equilibrium, low-temperature plasmas. The data types supported by LXCat are electron- and ion-scattering cross-sections with neutrals (total and differential), interaction potentials, oscillator strengths, and electron- and ion-swarm/transport parameters. Online tools allow users to identify and compare the data through plotting routines, and use the data to generate swarm parameters and reaction rates with the integrated electron Boltzmann solver. In this review, the historical evolution of the project and some perspectives on its future are discussed together with a tutorial review for using data from LXCat.

Population kinetics of many-electron atoms in ionizing plasmas studied using a continuous collisional radiative model

Collisional radiative (CR) models based on ab initio atomic structure calculation have been utilized over 20 years to analyze many-electron atomic and ionic spectra. Although the population distribution of the excited states in plasmas and their emission spectra are computed using CR models, systematic and analytical understanding of the population kinetics is still lacking. In this work, we present a reduced model of the population dynamics in many-electron atomic ions, in which we approximate the dense energy structure of complex many-electron atoms by a continuum, a continuous CR model (CCRM). Using this simplification, we show an analytical population distribution of many-electron atoms in plasmas and its electron-density and temperature dependence. In particular, the CCRM shows that the population distribution of highly excited states of many-electron atoms in plasmas resembles a Boltzmann distribution but with an effective excitation temperature. We also show the existence of three typical electron-density regions and two electron-temperature regions where the parameter dependence of the excitation temperature is different. Analytical representations of the effective excitation temperature and the boundaries of these phases are also presented.

Rayleigh and Raman Scattering from Alkali Atoms

Two computational methods developed recently [McNamara, Fursa, and Bray, Phys. Rev. A 98, 043435 (2018)] for calculating Rayleigh and Raman scattering cross sections for atomic hydrogen have been extended to quasi one-electron systems. A comprehensive set of cross sections have been obtained for the alkali atoms: lithium, sodium, potassium, rubidium, and cesium. These cross sections are accurate for incident photon energies above and below the ionization threshold, but they are limited to energies below the excitation threshold of core electrons. The effect of spin-orbit interaction, importance of accounting for core polarization, and convergence of the cross sections have been investigated.

Atomic Data for Plasma Spectroscopy: The CHIANTI Database, Improvements and Challenges

CHIANTI is an atomic database and software package for modeling emission lines and continua from hot astrophysical plasmas. It is freely available to all researchers and has been widely used in the Heliophysics and Astrophysics communities for almost 25 years. In this review, we summarize the properties of the current version of the database and give an overview of the relevant atomic processes. We also discuss progress towards a complete implementation of collisional-radiative modeling, simultaneously solving for atomic level and ion populations for individual elements.

Development of a multi-color gas puff imaging diagnostic on HL-2A tokamak

A Multi-Color (MC) gas puff imaging diagnostic has been developed on HL-2A tokamak. This diagnostic can simultaneously measure two-dimensional (2D, radial, and poloidal) electron density and temperature distributions with a good spatial resolution of 2.5 × 2.5 mm² and a temporal resolution of about 100 µs at best in edge plasmas. The 2D electron density and temperature distributions are inferred from the ratios of intensities of three different neutral helium emission lines; therefore, it is also referred to as helium beam probe or beam emission spectroscopy on thermal helium. A compact light splitter is used to split the inlet visible emission beam into four channels, and the specific neutral helium lines of the wavelengths λ₁ = 587.6 nm, λ₂ = 667.8 nm, λ₃ = 706.5 nm, and λ₄ = 728.1 nm are measured, respectively. This MC diagnostic has been experimentally tested and calibrated on a linear magnetic confinement device Peking University Plasma Test device, and the measured 2D electron density and temperature distributions are compared with the Langmuir probe measurements.

Triple differential cross sections for electron-impact ionization of methane at intermediate energy

We report an experimental and theoretical investigation of electron-impact single ionization of the highest occupied molecular orbital 1t₂ and the next highest occupied molecular orbital 2a₁ states of CH₄ at an incident electron energy of 250 eV. Triple differential cross sections measured in two different laboratories were compared with results calculated within the molecular 3-body distorted wave and generalized Sturmian function theoretical models. For ionization of the 1t₂ state, the binary peak was observed to have a single maximum near the momentum transfer direction that evolved into a double peak for increasing projectile scattering angles, as has been seen for ionization of atomic p-states. A detailed investigation of this evolution was performed. As expected because of its s-type character, for ionization of the 2a₁ state, only a single binary peak was observed. Overall, good agreement was found between experiment and theory.

Near-Threshold Cross Sections for Electron and Positron Impact Ionization of Atomic Hydrogen

Using classical arguments Wannier [Phys. Rev. 90, 817 (1953)PHRVAO0031-899X10.1103/PhysRev.90.817] proposed an electron-impact ionization cross section for neutral atoms to behave as E^{1.127}, where E is the excess energy above threshold. Using similar arguments Klar [J. Phys. B 14, 4165 (1981)JPAMA40022-370010.1088/0022-3700/14/21/027] obtained E^{2.65} to be the corresponding threshold law for positron impact. Recently, Babij et al. [Phys. Rev. Lett. 120, 113401 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.113401] measured near-threshold positron-impact breakup behavior to be similar to that expected for electrons. Using the convergent close-coupling method for the atomic hydrogen target, we examine cross sections at near-threshold energies for electron and positron impact. Contrary to the experiment, the calculated cross sections are found to behave differently for the two projectiles and consistently with the aforementioned threshold laws, despite the entirely quantum nature of these problems. For electron impact, the threshold behavior holds while the total electron spin asymmetry remains constant, whereas for positron scattering the threshold law holds for breakup while the positronium-formation component of the ionization cross section remains constant.

Solar UV and X-ray spectral diagnostics

X-ray and ultraviolet (UV) observations of the outer solar atmosphere have been used for many decades to measure the fundamental parameters of the solar plasma. This review focuses on the optically thin emission from the solar atmosphere, mostly found at UV and X-ray (XUV) wavelengths, and discusses some of the diagnostic methods that have been used to measure electron densities, electron temperatures, differential emission measure (DEM), and relative chemical abundances. We mainly focus on methods and results obtained from high-resolution spectroscopy, rather than broad-band imaging. However, we note that the best results are often obtained by combining imaging and spectroscopic observations. We also mainly focus the review on measurements of electron densities and temperatures obtained from single ion diagnostics, to avoid issues related to the ionisation state of the plasma. We start the review with a short historical introduction on the main XUV high-resolution spectrometers, then review the basics of optically thin emission and the main processes that affect the formation of a spectral line. We mainly discuss plasma in equilibrium, but briefly mention non-equilibrium ionisation and non-thermal electron distributions. We also summarise the status of atomic data, which are an essential part of the diagnostic process. We then review the methods used to measure electron densities, electron temperatures, the DEM, and relative chemical abundances, and the results obtained for the lower solar atmosphere (within a fraction of the solar radii), for coronal holes, the quiet Sun, active regions and flares.

Invited Review Article: Gas puff imaging diagnostics of edge plasma turbulence in magnetic fusion devices

Gas puff imaging (GPI) is a diagnostic of plasma turbulence which uses a puff of neutral gas at the plasma edge to increase the local visible light emission for improved space-time resolution of plasma fluctuations. This paper reviews gas puff imaging diagnostics of edge plasma turbulence in magnetic fusion research, with a focus on the instrumentation, diagnostic cross-checks, and interpretation issues. The gas puff imaging hardware, optics, and detectors are described for about 10 GPI systems implemented over the past ∼15 years. Comparison of GPI results with other edge turbulence diagnostic results is described, and many common features are observed. Several issues in the interpretation of GPI measurements are discussed, and potential improvements in hardware and modeling are suggested.

Attosecond Time Delay in Photoemission and Electron Scattering near Threshold

We study the time delay in the primary photoemission channel near the opening of an additional channel and compare it with the Wigner time delay in elastic scattering of the photoelectron near the corresponding inelastic threshold. The photoemission time delay near threshold is significantly enhanced, to a measurable 40 as, in comparison to the corresponding elastic scattering delay. The enhancement is due to the different lowest order of interelectron interaction coupling the primary and additional photoemission channels. We illustrate these findings by considering photodetachment from the H^{-} negative ion, and compare it with electron scattering on the hydrogen atom near the first excitation threshold. Other threshold processes of atomic photoionization and molecular photofragmentation, where photoemission time delay is enhanced, are identified. This opens the possibility of studying threshold behavior utilizing attosecond chronoscopy.

Complete Solution of Electronic Excitation and Ionization in Electron-Hydrogen Molecule Scattering

The convergent close-coupling method has been used to solve the electron-hydrogen molecule scattering problem in the fixed-nuclei approximation. Excellent agreement with experiment is found for the grand total, elastic, electronic-excitation, and total ionization cross sections from the very low to the very high energies. This shows that for the electronic degrees of freedom the method provides a complete treatment of electron scattering on molecules as it does for atoms.

Plasma pressure broadening for few-electron emitters including strong electron collisions within a quantum-statistical theory

To apply spectroscopy as a diagnostic tool for dense plasmas, a theoretical approach to pressure broadening is indispensable. Here, a quantum-statistical theory is used to calculate spectral line shapes of few-electron atoms. Ionic perturbers are treated quasistatically as well as dynamically via a frequency fluctuation model. Electronic perturbers are treated in the impact approximation. Strong electron-emitter collisions are consistently taken into account with an effective two-particle T-matrix approach. Convergent close-coupling calculations give scattering amplitudes including Debye screening for neutral emitters. For charged emitters, the effect of plasma screening is estimated. The electron densities considered reach up to n(e) = 10(27) m(-3). Temperatures are between T = 10(4) and 10(5) K. The results are compared with a dynamically screened Born approximation for Lyman lines of H and H-like Li as well as for the He 3889 Å line. For the last, a comprehensive comparison to simulations and experiments is given. For the H Lyman-α line, the width and shift are drastically reduced by the Debye screening. In the T-matrix approach, the line shape is notably changed due to the dependence on the magnetic quantum number of the emitter, whereas the difference between spin-scattering channels is negligible.

Invariant Graphical Method for Electron-Atom Scattering Coupled-Channel Equations

We present application examples of a graphical method for the efficient construction of potential matrix elements in quantum physics or quantum chemistry. The simplicity and power of this method are illustrated through several examples. In particular, a complete set of potential matrix elements for electron-lithium scattering are derived for the first time using this method, which removes the frozen core approximation adopted by previous studies. This method can be readily adapted to study other many-body quantum systems.

Fully relativistic convergent close-coupling method for excitation and ionization processes in electron collisions with atoms and ions

We report the development of the fully relativistic convergent close-coupling method based on the solution of the Dirac equation. A complete square-integrable Dirac L-spinor basis is used to obtain a set of target states spanning the target discrete and continuous positive- and negative-energy spectra. The present implementation is for quasi-one-electron atoms whose electronic configuration corresponds to the first column of the periodic table. By way of example, we consider elastic scattering of 7 eV electrons on the ground state of cesium, where the full set of spin asymmetries (A1, A2, Ann) has been measured. Excellent agreement with experiment is found.

Near-threshold positron-impact ionization of atomic hydrogen

We consider the positron-impact ionization (breakup) of atomic hydrogen utilizing the full and S-wave model calculations, concentrating on the near-threshold energy region. Unlike the corresponding electron-impact case, the S-wave model does support the Wannier-like threshold law predicted by Ihra et al. [Phys. Rev. Lett. 78, 4027 (1997)10.1103/PhysRevLett.78.4027]. It is found that convergent S-wave model cross sections are obtained only if complete expansions are utilized on both the atomic and the positronium centers. Furthermore, we suggest that, in the model and full calculations, the separate contributions to the breakup cross section from both centers become equal at threshold.

Close-coupling approach to Coulomb three-body problems

The convergent close-coupling method is shown to overcome the remaining discrepancies with experiment of electron-hydrogen ionization. Consequently, this method is able to calculate accurately the Coulomb three-body problems which include electron collisions with hydrogen and helium (within the frozen core model), and helium double photoionization at all incident energies and kinematical or geometrical arrangements of the outgoing electrons.

Absolute differential cross sections for photo double ionization of helium from the Ab initio hyperspherical R-matrix method with semiclassical outgoing waves

The hyperspherical R-matrix method with semiclassical outgoing waves introduced by us previously [Phys. Rev. A 60, 3667 (1999)] is applied to the one-photon double ionization of the He atom. The absolute differential cross sections obtained are in excellent agreement with experiment for the very challenging dynamical situations considered. This method is the first one to compute the final double continuum state accurately over the entire configuration space, from the vicinity of the nucleus to the asymptotic region.