M. J. Seaton

Computer programs for the calculation of electron-atom collision cross sections. I. General formulation

The wavefunction for electron collisions with an N-electron atom is expanded in the form Psi = Sigma i Theta i+ Sigma j Phi jcj where Theta i is an antisymmetrized product of an atomic eigenfunction times an orbital function theta i for the colliding electron; theta i contains a radial function Fi; Phi j has the form of a bound state function for the (N+1)-electron problem. The condition is imposed that (Pgamma mod Fi)=0 if lgamma =li, where Pgamma is an atomic radial function and where lgamma and li are orbital angular momenta associated with Pgamma and Fi; this condition does not imply a restriction on Psi so long as a suitable set of states Phi j is included. The variational principle is discussed and two approximations are described: (i) The distorted wave (DW) approximation is valid when the coupling is not too strong. Particular attention is paid to the normalization of the DW functions Fi. The coefficients cj are determined using the variational principle. (ii) The variational principle is used to obtain a set of coupled integro-differential (ID) equations for the determination of the functions Fi and the coefficients cj.

Atomic data for opacity calculations. IX. The lithium isoelectronic sequence

Bound-state energies, oscillator strengths and photoionisation cross sections have been calculated for members of the lithium isoelectronic sequence with nuclear charge Z in the range 3<or=Z<or=10. Two independent approaches to the problem give virtually the same results. Detailed comparisons with experiment and other theoretical results indicate that the present data are of high accuracy.

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.

Opacity Project data on CD for mean opacities and radiative accelerations

All monochromatic opacity data from the Opacity Project (OP), together with all codes required for the calculation of mean opacities and radiative accelerations for any required chemical mixture, temperature and mass density, are being put on a 700-MB CD which will be made generally available. The present letter gives a concise summary of the contents of the CD. More complete documentation will be provided on the CD itself.

Atomic data for opacity calculations. VIII. Line-profile parameters for 42 transitions in Li-like and Be-like ions

Widths and shifts are calculated in the electron impact approximation, using close-coupling theory, for the transitions 2s-2p, 2s-3p, 2p-3s, 2p-3d, 3s-3p and 3p-3d in Be II, B III, C IV, O VI and Ne VIII, and the transitions 2s2 1S-2s2p 1Po, 2s2p 3Po-2p2 3P, 2s2p 1Po-2p2 1D and 1S in C III, O V and Ne VII. Results are compared with those from previous calculations and from experiments. Approximate formulae must be used to estimate linewidths for some 106 transitions which are of importance for the calculation of stellar envelope opacities. Results for the quantum mechanical calculations for 42 transitions are used to obtain provisional best estimates for the parameters in these formulae.

Atomic data for opacity calculations. XIII. Line profiles for transitions in hydrogenic ions

For pt.XII see ibid., vol.22, p.3603 (1989). Methods are described for the calculation of profiles of lines due to transitions in hydrogenic ions. Requirements are that the calculations should be fast and should give results of accuracy adequate for the opacity work, for which the line wings are of particular importance. Quantum mechanical methods are used for the electron perturbers and a quasi-static theory is used for the ion perturbers. Results of the calculations are compared with measured profiles for H I and He II lines. The agreement is generally satisfactory. There are some discrepancies in the line cores, due to neglect of ion dynamics, but these are not of importance for the opacity work.

On the importance of inner-shell transitions for opacity calculations

For high temperatures and densities, stellar opacities obtained from the Opacity Project (OP) were smaller than those obtained from the OPAL project. Iglesias and Rogers (1995 Astrophys. J. 443 469) suggested that the discrepancy was due to the omission by OP of important atomic inner-shell processes, and considered in detail results for a mixture of six elements: H, He, C, O, S and Fe. Extensive new inner-shell data have now been computed using the code AUTOSTRUCTURE. It is shown that the inclusion of these data in the OP work gives opacities for the six-element mix which are in much closer agreement with those from OPAL. We also discuss a number of problems relating to the calculation of opacities and of equations of state for dense plasmas.

Computer programs for the calculation of electron-atom collision cross sections. II. A numerical method for solving the coupled integro-differential equations

For pt.I, see abstr. A7075 of 1973. The coupled integro-differential equations, described in Paper I, are reduced to linear algebraic equations. The finite difference formulae used are described in detail. The linear algebraic equations are solved using a technique which has good numerical stability and which gives good linear independence in the solution vectors. The method is economic in the use of computer time and storage.

OPserver: interactive online computations of opacities and radiative accelerations

Codes to compute mean opacities and radiative accelerations for arbitrary chemical mixtures using the Opacity Project recently revised data have been restructured in a client‐server architecture and transcribed as a subroutine library. This implementation increases efficiency in stellar modelling where element stratification due to diffusion processes is depth dependent, and thus requires repeated fast opacity re-estimates. Three user modes are provided to fit different computing environments, namely, a web browser, a local workstation and a distributed grid.

QUANTUM DEFECT THEORY. VII. ANALYSIS OF RESONANCE STRUCTURES.

The scattering matrix for electron collisions with positive ions may be expressed in terms of a matrix R which varies slowly as a function of the energy. In the neighbourhood of resonances the scattering matrix varies rapidly. Resonances associated with a single closed channel, or with a group of degenerate closed channels, are analysed using a method similar to that published by Gailitis in 1963. It is shown that the poles of the scattering matrix are given by a Rydberg formula containing a complex quantum defect. The case of non-degenerate closed channels is also discussed. For electron collisions with highly ionized atoms the R matrix may be calculated using perturbation theory. It is shown that, in this limit, the resonant and non-resonant contributions to excitation rates are of comparable order of magnitude.