D. M. Mitnik

Dielectronic Recombination Data for Dynamic Finite-Density Plasmas. I; Goals and Methodology

A programme is outlined for the assembly of a comprehensive dielectronic recombination database within the generalized collisional-radiative (GCR) framework. It is valid for modelling ions of elements in dynamic finite-density plasmas such as occur in transient astrophysical plasmas such as solar flares and in the divertors and high transport regions of magnetic fusion devices. The resolution and precision of the data are tuned to spectral analysis and so are sufficient for prediction of the dielectronic recombination contributions to individual spectral line emissivities. The fundamental data are structured according to the format prescriptions of the Atomic Data and Analysis Structure (ADAS) and the production of relevant GCR derived data for application is described and implemented following ADAS. The requirements on the dielectronic recombination database are reviewed and the new data are placed in context and evaluated with respect to older and more approximate treatments. Illustrative results validate the new high-resolution zero-density dielectronic recombination data in comparison with measurements made in heavy-ion storage rings utilizing an electron cooler. We also exemplify the role of the dielectronic data on GCR coefficient behaviour for some representative light and medium weight elements.

Electron-impact excitation of Ne +

We present the results of a 61-term, 138-level intermediate-coupling frame-transformation R-matrix close-coupling calculation of the electron-impact excitation of fluorine-like Ne+. All levels of the 2s22p5, 2s2p6, 2s22p43l and 2s22p44l configurations that lie below the ionization limit are included in the close-coupling expansion. With the exception of several R-matrix calculations of excitation between the fine structure levels of 2s22p5 2P, this represents the first close-coupling calculation for this ion. Here we describe this calculation and present radiative rates and effective collision strengths for a selected number of the 9453 transitions resulting from this work. The full set of data is available at the Oak Ridge National Laboratory Controlled Fusion Atomic Data Center Web site.

The time-dependent close-coupling method for atomic and molecular collision processes

We review the development of the time-dependent close-coupling method to study atomic and molecular few body dynamics. Applications include electron and photon collisions with atoms, molecules, and their ions.

Dielectronic recombination data for dynamic finite-density plasmas

Partial and total dielectronic recombination (DR) rate coefficients for fluorine-like ions forming neon-like systems have been calculated as part of the assembly of a final-state level-resolved DR database necessary for the modelling of dynamic finite-density plasmas (Badnell et al. 2003). Calculations have been performed for DR of both ground and metastable initial states for Ne to Zn21+, as well as for Kr27+, Mo33+, and Xe45+. Results for a selection of ions are presented and discussed. We find that low-temperature DR, via 2 → 2 core excitations involving no change in the principal quantum number of the core electron, does not scale smoothly with nuclear charge Z due to resonances straddling the ionization limit of the recombined system, thereby making explicit calculations for each ion necessary. Most of the earlier calculations neglected contributions from the fine-structure 2p3/2 − 2p1/2 excitation which has been shown to be very important for low-temperature DR coefficients. The DR data are suitable for modelling of solar and cosmic plasmas under conditions of collisional ionization equilibrium, photoionization equilibrium, and non-equilibrium ionization.

Dielectronic recombination data for dynamic finite-density plasmas. VIII. The nitrogen isoelectronic sequence

Dielectronic recombination data for nitrogen-like ions forming oxygen-like ions has been calculated as part of the assembly of a level-resolved dielectronic recombination database necessary for the modelling of dynamic finite-density plasmas (Badnell et al. 2003). Dielectronic recombination rate coefficients for a selection of ions from O + to Xe 47+ are presented and the results discussed.

Computational methods for Generalized Sturmians basis

Article history: The computational techniques needed to generate a two-body Generalized Sturmian basis are described. These basis are obtained as a solution of the Schrodinger equation, with two-point boundary conditions. This equation includes two central potentials: A general auxiliary potential and a short-range generating potential. The auxiliary potential is, in general, long-range and it determines the asymptotic behavior of all the basis elements. The short-range generating potential rules the dynamics of the inner region. The energy is considered a fixed parameter, while the eigenvalues are the generalized charges. Although the finite differences scheme leads to a generalized eigenvalue matrix system, it cannot be solved by standard computational linear algebra packages. Therefore, we developed computational routines to calculate the basis with high accuracy and low computational time. The precise charge eigenvalues with more than 12 significant figures along with the corresponding wave functions can be computed on a single processor within seconds.

Electron-impact excitation of Fe21+, includingn= 4 levels

We have carried out a 204-level close-coupling (CC) calculation for B-like Fe using the R-matrix method in conjunction with the intermediate-coupling frame transformation method as part of the RmaX Network programme of work to provide atomic data for x-ray processes. We have also carried out two 125-level CC calculations to enable us to illustrate the effect of n = 4 levels on collision data involving n = 2 and 3 levels and to provide a quantitative guide to the uncertainty resulting from the partial resolution of resonances. From our 204-level CC calculation, we have generated effective collision strengths over T = 10 5 –10 8 K for all 20 706 inelastic transitions, which is an order of magnitude larger than has been generated hitherto. We provide illustrative comparisons with the results of previous workers, where possible, and find a broad accord. The consistent and comprehensive set of data that we have generated (energy levels, radiative rates and effective collision strengths, including Born limits) is of great relevance to studies utilizing spectral observations from the new high-resolution x-ray satellites Chandra and XMM–Newton, as well as being necessary for the collisional– radiative modelling of metallic impurities that will arise in the next generation of magnetic fusion reactors.

An R -matrix with pseudo-states calculation of electron-impact excitation in C 2 +

We have performed an R-matrix with pseudo-states (RMPS) calculation of electron-impact excitation in C2+. Collision strengths and effective collision strengths were determined for excitation between the lowest 24 terms, including all those arising from the 2s3l and 2s4l configurations. In the RMPS calculation, 238 terms (90 spectroscopic and 148 pseudo-state) were employed in the close-coupling (CC) expansion of the target. In order to investigate the significance of coupling to the target continuum and highly excited bound states, we compare the RMPS results with those from an R-matrix calculation that incorporated all 238 terms in the configuration-interaction expansion, but only the lowest 44 spectroscopic terms in the CC expansion. We also compare our effective collision strengths with those from an earlier 12-state R-matrix calculation (Berrington et al 1989 J. Phys. B: At. Mol. Opt. Phys. 22 665). The RMPS calculation was extremely large, involving (N + 1)-electron Hamiltonian matrices of dimension up to 36 085, and required the use of our recently completed suite of parallel R-matrix programs. The full set of effective collision strengths from our RMPS calculation is available at the Oak Ridge National Laboratory Controlled Fusion Atomic Data Center web site.

Chapter 7 – Three-Body Coulomb Problems with Generalized Sturmian Functions

Abstract The study of structure and collision processes of three- and four-body problems has seen an extraordinary progress in the last decades. This progress has been in part associated to the incredible fast growth of the computer capabilities. However, the tools used to solve structure problems are different from those corresponding to the treatment of collision processes. In this review, we provide the theoretical framework and a selection of results for both structure as well as collision problems using only one technique that we have developed in the last few years, based on the use of Generalized Sturmian functions. We present results obtained in structure studies of isolated and confined two-electron atoms, and exotic and molecular systems. The same technique is applied to the study of various benchmark problems for the single ionization of hydrogen and the double ionization of helium by electron impact. In this way, we demonstrate that the Generalized Sturmian method can be successfully applied to the treatment of both types of problems.

Double ionization of helium by fast electrons with the Generalized Sturmian Functions method

The double ionization of helium by high energy electron impact is studied. The corresponding four-body Schrodinger equation is transformed into a set of driven equations containing successive orders in the projectile–target interaction. The first order driven equation is solved with a generalized Sturmian functions approach. The transition amplitude, extracted from the asymptotic limit of the first order solution, is equivalent to the familiar first Born approximation. Fivefold differential cross sections are calculated for (e, 3e) processes within the high incident energy and small momentum transfer regimes. The results are compared with other numerical methods, and with the only absolute experimental data available. Our cross sections agree in shape and magnitude with those of the convergent close coupling method for the (10+10) eV and (4+4) eV emission energies. To date this had not been achieved by any two different numerical schemes when solving the three–body continuum problem for the fast projectile (e, 3e) process. Though agreement with the experimental data, in particular with respect to the magnitude, is not achieved, our findings partly clarify a long standing puzzle.