K A Berrington

Atomic data for opacity calculations. II. Computational methods

For pt.I see ibid., vol.20, p.6363-78 (1987). A general description of the data requirements for opacity calculations has been given in paper I. The present paper gives a detailed description of the methods being used in a collaborative effort which is referred to as the Opacity Project. The close-coupling approximation of electron-atom collision theory is used to calculate energies and wavefunctions for bound states, oscillator strengths, photoionisation cross sections and parameters for line broadening by electron impact. The computations are made using the R-matrix method together with new codes for calculating outer-region solutions and dipole integrals. Use of these techniques provides an efficient means of calculating large amounts of accurate atomic data.

Atomic data for opacity calculations. XIV. The beryllium sequence

The authors have calculated 1814 energy levels in LS coupling, 33030 oscillator strengths and 859570 photoionization cross section values for the following fifteen members of the beryllium isoelectronic sequence: Be I, B II, C III, N IV, O V, F VI, Ne VII, Na VIII, Mg IX, Al X, Si XI, S XIII, Ar XV, Ca XVII and Fe XXIII. Photoionization is from 1554 bound states lying below the 2s ionization thresholds. The continua are perturbed by resonances converging onto the 2p, 3s, 3p and 3d states of the residual Li-like ions. They delineate the resulting autoionization features by using sufficiently small energy step lengths in regions where the cross sections vary rapidly. Photoexcitation of the core produces large PEC resonances which dominate photoionization of Be I and the less highly ionized ions. They discuss some selected examples drawn from the entire data set and make comparisons with the work of other investigators.

Electron-impact-excitation collision strengths for Be-like ions: II. Intermediate-energy region and collision rates

Abstract Intermediate-energy collision strengths calculated using the R-matrix method are presented for four Be-sequence ions, C III (2.6–8.0 Ry), O V (4.4–12.0 Ry), Ne VII (8.4–20.0 Ry), and Si XI (11.0–34.0 Ry). The six ionic states (2s2) 1S, (2s2p)3P0, 1P0 and (2p2)3Pe, 1De, 1Se, corresponding to ten fine-structure levels, are included, leading to 29 independent transitions per ion. High-energy analytical expressions have also been calculated for the collision strengths. These results have been combined with previously published low-energy collision strengths to deduce effective collision strengths (that is, collision rates) for ranges of electron temperature appropriate to the four ions.

Improved calculations for the C III 1907,1909 and Si III 1883,1892 electron density sensitive emission-line ratios, and a comparison with IUE observations

Atomic data are used in conjunction with the statistical equilibrium code of Dufton (1977) to calculate relative C III and Si III level populations, and hence emission-line strengths for a range of electron temperatures and densities. It is assumed that photoexcitation and deexcitaton rates are negligible in comparison with the corresponding collisional rates, that ionization to and recombination from other ionic levels are slow compared with bound-bound rates, and that all transitions are optically thin. The observed values of R1 and R2 for several planetary nebulae and a symbiotic star, measured from high-resolution spectra obtained with the IUE satellite, lead to electron densities that are compatible, and are also in good agreement with those deduced from line ratios in other species.

The scattering of electrons by atomic nitrogen

Cross sections for elastic and inelastic scattering of electrons by atomic nitrogen are calculated over an incident electron energy range from threshold to 35 eV using the R-matrix method. In most of the calculations the eight target states 1s22s2p3 4S0 2D0 and 2P0, 1s22s2p4 4Pe 2Pe 2De and 2Se and 1s22p5 2P0 of nitrogen are retained in the expansion of the total wavefunction. However in some of the calculations fewer target states are retained in order to compare with the results of earlier work. Apart from energies close to the 1s22s22p4 3Pe resonance state of N- the cross sections appear to have converged well.

Electron-Atom Scattering at Intermediate Energies

Over the last few years there has been much interest, both theoretically and experimentally, in electron-atom scattering at intermediate energies. The theoretical work has been driven mainly by the many applications in astronomy, laser physics and plasma physics which require accurate data for their interpretation and by experimental advances which provide an important stimulus to theory. The increasing availabililty of more powerful computers has enabled the development of more sophisticated theoretical methods to study electron scattering in the intermediate energy regime, which faces particular difficulties owing to the infinite number of open channels which occur in this energy region. In order to obtain accurate results in the intermediate energy region, the theoretical approaches used must be able, in some way, to allow for loss of flux into these highly excited states and continuum states of the target atom or ion. Recent theoretical approaches which have been proposed include extensions of low-energy methods, the use of optical potentials and extensions of the Born approximation by the inclusion of higher-order terms.

Free-free absorption coefficient of the negative hydrogen ion

The free-free absorption coefficient of the negative ion of hydrogen is calculated within the framework of the R-matrix method. The 1s, 2s and 2p states of hydrogen together with three pseudostates have been employed in the eigenfunction expansion. The results have been found to be in good agreement with other calculations and are believed to be currently the most accurate available.

Total cross sections for electron excitation transitions between the 11S, 23S, 21S, 23P and 21P states of atomic helium

The five-state R-matrix calculations of Berrington et al. (1975) on the excitation of helium by electrons have been revised and extended to higher electron impact energies. Inelastic scattering cross sections are presented for all transitions between the 11S, 23S, 21S, 23P and 21P states of helium, and elastic cross sections are presented for the n=2 states.

Electron collisional excitation of C III and O V

The R-matrix method is being used to determine the collisional excitation cross sections between the 2s2 1Se, 2s2p 3Po, 1Po and the 2p2 3Pe, 1De, 1Se target eigenstates of the beryllium isoelectronic sequence. The first results for the 2s2 1S3-2s2p 3Po and 2s2 1Se-2s2p 1Po transitions for C III and O V are presented and compared with earlier distorted-wave and close-coupling results. The results indicate that the use of accurate target eigenstates and a more accurate treatment of the collision problem may change the cross sections by as much as 20% from earlier work.

Electron collision cross sections at low energies for all transitions between the n=1, 2, 3, 4 and 5 levels of atomic hydrogen

Collision strengths for all transitions among states up to the n=5 level are reported in the energy range below 1.96 Ryd. The R-matrix and no-exchange programs have been used for partial waves with L 9 respectively. The results are analysed in detail highlighting the resonance structure. They are also compared with other results. The effective collision strengths obtained after averaging the collision strengths over a Maxwellian distribution of electron velocities are listed at temperatures below 50000 K. Though the results require an improvement especially in the intermediate energy region, nevertheless they are probably the best available for most of the transitions.