Dirac B-spline R-matrix Research Articles

Insights from Collisional-Radiative Models of Neutral and Singly Ionized Xenon in Hall Thrusters

Collisional-radiative (CR) models for neutral and singly ionized xenon have been constructed for applications to Hall thruster diagnostics. The models use primarily theoretical electron-impact excitation cross sections calculated using the Dirac B-spline R-matrix method. This paper describes the models’ construction and their validation against heritage CR models and previously published Hall thruster data, and then outlines several applications. The baseline 0D steady-state models are used to investigate electron density dependence in neutral xenon emission line intensity ratios commonly used to measure electron temperature, and also to demonstrate that stepwise ionization through excited states is an important process in Hall thrusters. The models are extended to evaluate impacts of neutral and ion transport on 0D CR model applicability, intrinsic bandwidth limits for time-dependent line intensity measurements, and errors introduced when the plasma is assumed to be optically thin.

Electron-impact excitation of the 5varvec{^2textbf{S}_{1/2} rightarrow 5^2textbf{P}_{1/2}} and 5varvec{^2textbf{P}_{3/2}} transitions in rubidium by 40 eV electrons: theory and experiment

We report on a series of detailed Breit-Pauli and Dirac B-spline R-matrix (DBSR) differential cross section (DCS) calculations for excitation of the 5,^2textrm{S}_{1/2} rightarrow 5,^2textrm{P}_{1/2} and 5,^2textrm{S}_{1/2}rightarrow 5,^2textrm{P}_{3/2} states in rubidium by 40 eV incident electrons. The early BP computations shown here were carried out with both 5 states and 12 states, while the DBSR models coupled 150 and 325 states, respectively. We also report corresponding results from a limited set of DCS measurements on the unresolved 5,^2textrm{P}_{1/2,3/2} states, with the experimental data being restricted to the scattered electron angular range 2–10^circ . Typically, good agreement is found between our calculated and measured DCS for excitation of the unresolved 5,^2textrm{P}_{1/2,3/2} states, with best accord being found between the DBSR predictions and the measured data. The present theoretical and experimental results are also compared with predictions from earlier 40 eV calculations using the nonrelativistic Distorted-Wave Born Approximation and a Relativistic Distorted-Wave model.Graphic abstract

Relativistic B-Spline R-Matrix Calculations for Electron Scattering from Thallium Atoms

The Dirac B-spline R-matrix (DBSR) method is employed to treat low-energy electron collisions with thallium atoms. Special emphasis is placed on spin polarization phenomena that are investigated through calculations of the differential cross-section and the spin asymmetry function. Overall, good agreement between the present calculations and the available experimental measurements is found. The contributions of electron exchange to the spin asymmetry cannot be ignored at low impact energies, while the spin–orbit interaction plays an increasingly significant role as the impact energy rises.

Relativistic B-Spline R-Matrix Calculations for Electron Collisions with Ytterbium

We have applied the full-relativistic Dirac B-Spline R-matrix method to obtain cross sections for electron scattering from ytterbium atoms. The results are compared with those obtained from a semi-relativistic (Breit-Pauli) model-potential approach and the few available experimental data.

Chemical diversity among A–B stars with low rotational velocities: non-LTE abundance analysis

ABSTRACT We present accurate element abundance patterns based on the non-local thermodynamic equilibrium (non-LTE, NLTE) line formation for 14 chemical elements from He to Nd for a sample of nine A9 to B3-type stars with well-determined atmospheric parameters and low rotational velocities. We constructed new model atom of Zr ii–iii and updated model atoms for Sr ii and Ba ii by implementing the photoionization cross-sections from calculations with the Dirac B-spline R-matrix method. The NLTE abundances of He to Fe in the stars HD 17081, HD 32115, HD 160762, and HD 209459 are found to be consistent with the solar abundances, and HD 73666 being a Blue Straggler does not reveal deviations from chemical composition of the Praesepe cluster. Three of these stars with an effective temperature of lower than 10 500 K have supersolar abundances of Sr, Zr, Ba, and Nd, and our results suggest the presence of a positive correlation between stellar effective temperature and abundance. For each star, enhancement of Ba is higher than that for any other heavy element. We propose that the solar Ba abundance is not representative of the galactic Ba abundance at modern epoch. The status of HD 145788 was not clarified: This star has solar abundances of C to Si and enhancements of Sr to Ba similar to that for superficially normal stars of similar temperature, while Ca, Ti, and Fe are overabundant. The NLTE abundances of Vega support its status of a mild λ Bootis star.

Cross sections for electron scattering from atomic lead

We applied the relativistic convergent close-coupling and the Dirac B-spline R-matrix methods to electron scattering from lead atoms. Differential and integrated cross sections are presented for elastic scattering and excitations from the ground state to the 6p7s, 6p7p, and 6p6d manifolds for energies ranging from 1 to 100 eV. The momentum-transfer, ionisation, and total scattering cross sections are also presented. Our results are compared with experimental data and previous theoretical predictions where available. Generally good agreement is found between the two theories and experiment, though some renormalisation of experiment is suggested.

A xenon collisional-radiative model applicable to electric propulsion devices: I. Calculations of electron-impact cross sections for xenon ions by the Dirac B-spline R-matrix method

A fully relativistic Dirac B-spline R-matrix (DBSR) method is applied to calculate the oscillator strengths and electron-impact excitation cross sections involving the 5s25p5, 5s5p6, 5p46s, 5p45d, 5p46p, and 5p47s states of a Xe+ ion. A fully relativistic approach is necessary for this problem, since the spin–orbit coupling is of the same order as electron correlations in the outer shells of Xe+. Also, there is a complex open-shell structure with strong term dependence in the one-electron orbitals. The oscillator strengths are also calculated and agree well with available experimental measurements. We select some important excitation cross sections out of the ground, metastable, and quasi-metastable states of Xe+ for the collisional-radiative (CR) model to be discussed and analyzed. The present paper is the first one of a series of studies on a CR model of xenon ions in plasma diagnosis and numerical simulations of Hall and ion thrusters. In subsequent papers, the cross-section data for the Xe+ ion, together with those for neutral Xe from our previous calculation, are used to build a comprehensive CR model for electric propulsion systems involving xenon. Furthermore, the predictions of this model will then be examined by experiments in both Hall and ion thrusters.

A xenon collisional-radiative model applicable to electric propulsion devices: II. Kinetics of the 6s, 6p, and 5d states of atoms and ions in Hall thrusters

Electric propulsion devices of using xenon propellant are nowadays widely adopted for the space missions. A collisional-radiative (CR) model of xenon needs to be developed to understand the kinetic mechanisms of the excited and energetic species in these devices and also to support their optical diagnostics. Previously, due to limitations in the fundamental cross section data, Xe CR models focused on the atomic species; the ionic species, which also play important roles for the thrusters, were not studied in detail. In our previous paper, a fully relativistic Dirac B-spline R-matrix method was applied to calculate the relevant cross sections for electron collisions with the Xe+ ion. Based on these data, a comprehensive CR model—with the kinetics of metastable and excited levels of both Xe and Xe+ included—could be built. The calculated density distributions of atomic and ionic levels are examined by optical measurements in Hall thrusters in all of the four typical regions (near-anode-, ionization-, acceleration-, and plume-region). The special kinetic behaviors of the excited species are analyzed, and a set of rate coefficient data used for the Xe CR model is also provided.

Relativistic B-spline R-matrix calculations for electron collisions with lead atoms: differential cross sections and spin asymmetries

The Dirac B-spline R-matrix (DBSR) method is employed to treat low-energy electron collisions with lead atoms. Very good agreement with the experimental data of Geesmann et al (1991 J. Phys. B: At. Mol. Opt. Phys. 24 2817) is obtained for the spin asymmetry function SA for elastic scattering from the (6p2)3P0 ground state as well as electron impact excitation of the (6p2)3P1 and (6p2)3P2 states. A very strong model sensitivity of the predictions for the (6p2)3P0 → (6p2)1D2 transition, on the other hand, explains the apparent difficulties in obtaining reliable results for this case. Angle-differential cross sections are also presented and compared with available experimental data.

Electron impact excitation of the lowest doublet and quartet core-excited autoionizing states in Rb atoms

Electron impact excitation of the (4p55s2)2P3/2,1/2 and (4p54d5s)4P1/2,3/2,5/2 autoionizing states in rubidium atoms was studied experimentally by measuring the ejected-electron excitation functions and theoretically by employing a fully relativistic Dirac B-spline R-matrix (close-coupling) model. The experimental data were collected in an impact energy range from the respective excitation thresholds up to 50 eV with an incident electron energy resolution of 0.2 eV and an observation angle of 54.7°. Absolute values of the excitation cross sections were obtained by normalizing to the theoretical predictions. The observed near-threshold resonance structures were also analysed by comparison with theory. For the 2P3/2,1/2 doublet states, a detailed analysis of the R-matrix results reveals that the most intense resonances are related to odd-parity negative-ion states with dominant configurations 4p55s5p2 and 4p54d5s6s. The measured excitation functions for the 2P1/2 and 4PJ states indicate a noticeable cascade population due to the radiative decay from high-lying autoionizing states. A comparative analysis with similar data for other alkali atoms is also presented.

Electron scattering from krypton: High-resolution experiments and B-spline R-matrix calculations

In a joint experimental and theoretical effort, we carried out a detailed study of e-Kr collisions. For elastic scattering and excitation of the 4p55s states, we present total and angle-differential cross sections over the entire angular range (0°-180°) for a number of energies, as well as energy scans for selected angles. The experimental results are in very satisfactory agreement with predictions from fully relativistic Dirac B-spline R-matrix models.

Resonance excitation of the (4p55s2)2P3/2,1/2 autoionizing states in Rb atoms by electron impact

The near-threshold excitation dynamics of the 4p55s2 2P3/2,1/2 autoionizing states in rubidium atoms was studied experimentally by measuring the ejected-electron excitation functions and theoretically by applying a fully relativistic Dirac B-spline R-matrix (close-coupling) model. As in the previously studied np5(n+1)s2 2P3/2,1/2 states in Na (n=2), K (n=3), and Cs (n=5) atoms, strong negative-ion resonances dominate the electron-impact excitation of the lowest autoionizing states in Rb.

High-resolution experiments andB-splineR-matrix calculations for elastic electron scattering from krypton

In a joint experimental and theoretical effort, we carried out a detailed study of elastic electron scattering from Kr atoms. Absolute angle-differential cross sections for elastic electron scattering were measured over the energy range 0.3-9.8 eV with an energy width of about 13 meV at scattering angles between 0 deg. and 180 deg. Excellent agreement is obtained between our experimental data and predictions from a fully relativistic Dirac B-spline R-matrix (close-coupling) model that accounts for the atomic dipole polarizability through a specially designed pseudostate.

Electron impact excitation of the (4p5 5s) states in krypton: high-resolution electron scattering experiments and -spline -matrix calculations

In a joint experimental and theoretical effort, we carried out a detailed study of electron impact excitation of the 4p5 5s states of Kr. We present angle-differential cross sections over the entire angular range (0°–180°) for a number of energies in the near-threshold region, as well as energy scans for selected angles. The experimental results are in very satisfactory agreement with predictions from a fully relativistic Dirac B-spline R-matrix model.

Fully relativistic B-spline R-matrix calculations for electron collisions with mercury atoms

Results from a fully relativistic 36-state Dirac B-spline R-matrix (close-coupling) calculation are reported and compared with experimental data for angle-integrated and angle-differential cross sections, as well as spin-polarization and electron-impact coherence parameters. In most cases we obtain significant improvement in the agreement between experiment and theory compared to previous distorted-wave and close-coupling attempts.

Fully relativistic B-spline R-matrix calculations for electron collisions with xenon atoms

Results from a fully relativistic 31-state Dirac B-spline R-matrix (close-coupling) calculation for e-Xe collisions are reported and compared with experimental data for angle-integrated and angle-differential cross sections, as well as spin-polarization and electron-impact coherence parameters. Particularly in the near-threshold resonance regime, we obtain significant improvement in the agreement between experiment and theory compared to previous distorted-wave and close-coupling attempts.

Resonance effects in electron and photon impact excitation of the p6 subvalence subshell in alkali atoms

Recent advances in the experimental and theoretical investigation of the excitation of the (np5(n + 1)s2)2P3/2,1/2 autoionizing states in alkali atoms is reported. These include a joint theoretical and experimental investigation of the lowest (5p56s2)2P3/2 autoionizing state in Cs, for which the ejected-electron excitation function was measured at an incident-electron energy resolution of 0.2 eV for impact energies up to 4 eV above the threshold, an improved R-matrix calculation for electron-impact excitation of the (3p54s2)2P3/2,1/2 leading autoionizing doublet in K, and a theoretical study of the inner-shell photodetachment of the Na− ion. The calculations for sodium and potassium were performed by employing a B-spline R-matrix (close-coupling) code in the semi-relativistic Breit–Pauli approximation, whereas the calculations for caesium were carried out with a new fully relativistic Dirac B-spline R-matrix program. All excitation functions reveal pronounced near-threshold resonance features, which were analysed and tentatively assigned on the basis of the present calculations.