V.M. Burke

Electron - atom scattering at low and intermediate energies using a pseudo-state/ R-matrix basis

The use of a pseudo-state expansion within the standard low-energy R-matrix framework to facilitate the study of electron scattering by complex atoms and ions at both low and intermediate energies is discussed. Electron scattering from atomic hydrogen is considered as an example, and results for elastic scattering phase shifts and excitation cross sections are found to be in excellent agreement with recent IERM results in these energy regions. The advantage of this procedure is that existing computer codes, which have been developed over many years, can be directly extended to study electron scattering from a general N-electron target atom or ion.

Farm — A flexible asymptotic R-matrix package

Abstract The R-matrix formalism has been highly successful in describing a wide range of atomic and molecular scattering problems. A computational bottleneck in these calculations is the treatment of the scattering in the external region of configuration space where exchange effects may be neglected. A new package for solving this external region scattering problem is described. The package uses a combination of R-matrix propagation techniques to ensure optimum stability and efficiency in integrating the coupled Schrodinger equations. The radial distance over which the equations must be integrated is minimized by matching to an asymptotic wavefunction determined by an accelerated Gailitis expansion. The package is designed to provide accurate results with minimal input information and to be efficient for large systems of equations.

A parallel R-matrix program PRMAT for electron–atom and electron–ion scattering calculations

Abstract This paper describes a new parallel R-matrix program PRMAT which enables very large electron–atom and electron–ion scattering calculations of importance in many applications to start to be addressed for the first time on the current generation of massively parallel computers. The paper commences with an overview of R-matrix theory applied to electron–atom and electron–ion scattering, in which the fundamental concepts and the basic equations of the theory are given. A detailed description of this new parallel program PRMAT is then given and its relation to earlier scalar programs RMATRXII and FARM, which treat respectively the internal and external R-matrix regions, is discussed. Of particular importance is the development of a new parallel spin-splitting algorithm and program which takes advantage of the spin de-coupling of the scattering channels in the external and asymptotic R-matrix regions where electron exchange and correlation effects are negligible. A detailed description of the allocation of processor nodes to the various parallel tasks is given and illustrative timings on a Cray T3E-1200 parallel supercomputer are given. Finally the paper concludes by describing an illustrative electron–NiIV ion scattering calculation of importance in the analysis of astronomical spectra. Converged effective collision strengths for some forbidden transitions are reported which involve the solution of cases with more than 300 coupled channels requiring the calculation of collision strengths at over 15,000 energy values.

Time-dependent R-matrix theory of multiphoton processes

A new time-dependent R-matrix theory of multiphoton processes is described which can be applied to an arbitrary many-electron atom. The theory is complementary to the R-matrix Floquet theory developed by Burke, Francken and Joachain (1991 J. Phys. B: At. Mol. Opt. Phys. 24 761) enabling processes involving higher laser field intensities and shorter laser pulses to be treated. The new theory is illustrated by analysing the multiphoton ionization of a charged particle bound initially in a one-dimensional potential well where the results are compared with an independent R-matrix Floquet calculation.

Electron impact excitation of Fe II : Total LS effective collision strengths

We present total effective collision strengths for electron-impact excitation of Fe II, calculated using the parallel R-matrix program PRMAT, for all sextet to quartet forbidden transitions among the lowest 113 LS states formed from the 3d64s, 3d7, 3d54s2, 3d64p and 3d54s4p basis configurations. After a detailed and systematic study of configuration-interaction effects in both the target and the collision wavefunctions, it was found that an additional 21 configurations needed to be included in the CI expansion to obtain significantly more accurate target state and collision wavefunctions. A total of 1785 individual lines are considered over a wide range of electron temperatures, 30–100 000 K, of particular importance in astrophysical applications. A detailed comparison is made with a previous 3 configuration approximation and significant differences of up to a factor of 2 are reported at the lowest temperatures considered. The inclusion of the additional 3d54s2 and 3d54s4p levels in the present work together with the additional CI effects are found to cause significant changes to the total effective collision strengths for the low-lying transitions from the ground state, particularly at very low temperatures. The disparities are found to be considerably less at the higher temperatures considered.

Differential cross sections and electron-impact coherence parameters for electron scattering from helium atoms

We have applied the R-matrix with pseudo-states method (RMPS) to study electron - helium scattering at intermediate energies. Differential cross sections for elastic and inelastic collisions and electron-impact coherence parameters for excitation of the transition are presented for incident energies of 30, 50 and 80 eV. Excellent agreement with experiment and with the predictions of the convergent close-coupling calculation by Fursa and Bray is obtained. Since correlation effects and target continuum states are both accurately represented in a completely general way by this method, the associated program package can now be used to obtain reliable results at intermediate energies for arbitrary complex atomic and ionic targets of importance in applications.

Configuration Interaction Effects in low-energy electron collisions with Fe II

Partial wave collision strengths are presented for low-energy electron-impact transitions in Fe II between the 3d 6 4 sa 6 D e ground state and the 3d 7 a 4 F e , 3d 6 4s a 4 D e and 3d 7 a 4 P e low-lying excited states. The collision strengths are calculated in LS coupling using a new Fortran 95 R-matrix program including all terms of the 3d 6 4s, 3d 7 , 3d 6 4p, 3d 5 4s 2 and 3d 5 4s4p configurations in the close coupling expansion of the collision wavefunction. Special emphasis is given to the inclusion of configuration interaction (CI) effects both in the target and in the collision wavefunctions. In both cases series of calculations are carried out where additional CI terms are included systematically. It is found that in order to obtain close to converged low-energy partial wave collision strengths two-electron excitations from the 3p shell to the 3d shell as well as pseudo s and d orbitals must be included in the CI expansions. Also resonance effects in low-energy partial wave collision strengths are found to depend sensitively on the representation of the d orbitals in the CI expansion of the collision wavefunction. Finally, CI models for both the target and collision wavefunctions are defined which can be used in proposed calculations to obtain accurate total collision strengths and effective collision strengths for transitions between LS-coupled terms and between fine-structure levels of Fe II.

Electron-impact excitation of the levels of carbon

The R-matrix method is used to investigate electron-impact excitation of neutral carbon over an energy range of interest for fusion plasma modelling. Two independent calculations are carried out. In the first, all levels of carbon with are included in the expansion of the total wavefunction and cross sections including exchange are calculated for collision energies from threshold to 150 eV. In the second, all levels with are included in the expansion and spin-allowed cross sections excluding exchange are calculated from threshold to 60 eV. Cross sections and effective collision strengths are presented for important transitions.

Graphical R-matrix atomic collision environment (GRACE): the problem specification stage

Abstract In this paper we introduce the concept of a graphical R-matrix atomic collision environment (GRACE). GRACE couples the graphical capability of powerful workstations with the processing power of supercomputers to provide an environment for the study of atomic collision properties and processes. At the core of GRACE is a new generation R-matrix program package, which is used to compute properties characterising electron atom and electron ion collisions. One of the motivations behind the project is to render this package simple to use by novice and experienced users alike, thereby significantly improving its usefulness to the physics community. GRACE is composed of a problem specification stage, a computation stage, and an interpretation stage. The focus of this paper is a description of the X Window graphical user interface which constitutes the problem specification stage of GRACE.

Electron-impact excitation of Fe II

We report in this paper the computation of accurate total collision strengths and effective collision strengths for electron-impact excitation of FeII, using the parallel R-matrix program PRMAT. Target states corresponding to the 3d64s, 3d7, 3d64p and 3d54s4s basis configurations were included in the calculations giving rise to a 113 LS state 354 coupled channel problem. Following a detailed systematic study of correlation effects in both the target state and collision wavefunctions, it was found that an additional 21 configuration functions needed to be included in the Configuration Interaction expansion to obtain significantly more accurate target states and collision wavefunctions. This much improved 26-configuration model has been used to calculate converged total effective collision strengths for all sextet to quartet transitions among these levels with total spin S = 2, giving a total of 1785 lines. These calculations have laid the foundation for an approach which may be adopted in the study of electron collisions with the low ionization stages of other iron peak elements. The work has been further extended with the commencement of a Breit-Pauli relativistic calculation for one of the smaller models and includes 262 fine-structure levels and over 1800 coupled channels. At the same time the PRMAT parallel R-matrix package is being extended to include relativistic effects which will allow us to attempt the more sophisticated 26-configuration model and produce for the first time the amount and quality of atomic data required to perform a meaningful synthesis of the Fe II spectrum.