T. W. Gorczyca

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.

COLLISIONAL IONIZATION EQUILIBRIUM FOR OPTICALLY THIN PLASMAS. I. UPDATED RECOMBINATION RATE COEFFICIENTS FOR BARE THROUGH SODIUM-LIKE IONS

Reliably interpreting spectra from electron-ionized cosmic plasmas requires accurate ionization balance calculations for the plasma in question. However, much of the atomic data needed for these calculations have not been generated using modern theoretical methods and are often highly suspect. This translates directly into the reliability of the collisional ionization equilibrium (CIE) calculations. We make use of state-of-the-art calculations of dielectronic recombination (DR) rate coefficients for the hydrogenic through Na-like ions of all elements from He up to and including Zn. Where measurements exist, these published theoretical DR data agree with recent laboratory work to within typically 35% or better at the temperatures relevant for CIE. We also make use of state-of-the-art radiative recombination (RR) rate coefficient calculations for the bare through Na-like ions of all elements from H through to Zn. Here we present improved CIE calculations for temperatures from 104 to 109 K using our data and the recommended electron impact ionization data of Mazzotta et al. for elements up to and including Ni and Mazzotta for Cu and Zn. DR and RR data for ionization stages that have not been updated are also taken from these two additional sources. We compare our calculated fractional ionic abundances using these data with those presented by Mazzotta et al. for all elements from H to Ni. The differences in peak fractional abundance are up to 60%. We also compare with the fractional ionic abundances for Mg, Si, S, Ar, Ca, Fe, and Ni derived from the modern DR calculations of Gu for the H-like through Na-like ions, and the RR calculations of Gu for the bare through F-like ions. These results are in better agreement with our work, with differences in peak fractional abundance of less than 10%.

High-Resolution X-Ray Spectroscopy of the Interstellar Medium. II. Neon and Iron Absorption Edges

We present high-resolution spectroscopy of the neon K-shell and iron L-shell interstellar absorption edges in nine X-ray binaries using the High Energy Transmission Grating Spectrometer (HETGS) on board the Chandra X-Ray Observatory. We found that the iron absorption is well fit by an experimental determination of the cross section for metallic iron, although with a slight wavelength shift of ≈20 mA. The neon edge region is best fit by a model that includes the neutral neon edge and three Gaussian absorption lines. We identify these lines as due to the 1s-2p transitions from Ne II, Ne III, and Ne IX. As we found in our oxygen edge study, the theoretical predictions for neutral and low-ionization lines all require shifts of ≈20 mA to match our data. Combined with our earlier oxygen edge study, we find that a best-fit O/Ne ratio of 5.4 ± 1.6, consistent with standard interstellar abundances. Our best-fit Fe/Ne ratio of 0.20 ± 0.03 is significantly lower than the interstellar value. We attribute this difference to iron depletion into dust grains in the interstellar medium. We make the first measurement of the neon ionization fraction in the ISM. We find Ne /Ne ≈ 0.3 and Ne /Ne ≈ 0.07. These values are larger than is expected given the measured ionization of interstellar helium. For Ne IX, our results confirm the detection of the hot ionized interstellar medium of the Galaxy.

K-Shell Photoabsorption of Oxygen Ions

Extensive calculations of the atomic data required for the spectral modeling of the K-shell photoabsorption of oxygen ions have been carried out in a multicode approach. The present level energies and wavelengths for the highly ionized species (electron occupancies 2 ≤ N ≤ 4) are accurate to within 0.5 eV and 0.02 A, respectively. For N > 4, lack of measurements, wide experimental scatter, and discrepancies among theoretical values are handicaps in reliable accuracy assessments. The radiative and Auger rates are expected to be accurate to 10% and 20%, respectively, except for transitions involving strongly mixed levels. Radiative and Auger dampings have been taken into account in the calculation of photoabsorption cross sections in the K-threshold region, leading to overlapping Lorentzian shaped resonances of constant widths that cause edge smearing. The behavior of the improved opacities in this region has been studied with the XSTAR modeling code using simple constant density slab models and is displayed for a range of ionization parameters.

Dielectronic recombination data for dynamic finite-density plasmas II. The oxygen isoelectronic sequence

Dielectronic recombination (DR) and radiative recombination (RR) data for oxygen-like ions forming fluorine-like ions have been calculated as part of the assembly of a level-resolved DR and RR database necessary for modelling of dynamic finite-density plasmas (Badnell et al. 2003). Total DR and RR rate coecients for F + to Zn 22+ are presented and the results discussed. By comparison between perturbative and R-matrix results, we find that RR/DR interference eects are negligible even for the lowest-charged F + member. We also find that the 2 ! 2 low-temperature DR (no change in the principal quantum number of the core electrons) does not scale smoothly with nuclear charge Z due to resonances straddling the ionization limit, thereby making explicit calculations for each ion necessary. These RR and 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 IV. The carbon isoelectronic sequence

Dielectronic recombination (DR) and radiative recombination (RR) data for carbon-like ions forming nitrogen-like ions have been calculated as part of the assembly of a level-resolved DR and RR database necessary for modelling of dynamic finite-density plasmas (Badnell et al. 2003). Total DR and RR rate coefficients are presented and the results discussed for N + to Zn 24+ ,a s well as Kr 30+ ,M o 36+ ,C d 42+ ,a nd Xe 48+ . We find that the 2 → 2 (no change in the principal quantum number of the core electron) low-temperature DR does not scale smoothly with nuclear charge Z due to resonances straddling the ionization limit, thereby making explicit calculations for each ion necessary. The RR and 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

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: IX. The fluorine isoelectronic sequence

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 2p(3/2)-2p(1/2) 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 (via N=2 -> N '=2 core excitations) and radiative recombination of Fe XX: Laboratory measurements and theoretical calculations

We have measured the resonance strengths and energies for dielectronic recombination (DR) of Fe xx forming Fe xix via N ¼ 2 ! N 0 ¼ 2( DN ¼ 0) core excitations. We have also calculated the DR resonance strengths and energies using the AUTOSTRUCTURE, Hebrew University Lawrence Livermore Atomic Code (HULLAC), Multiconfiguration Dirac-Fock (MCDF), and R-matrix methods, four different state-ofthe-art theoretical techniques. On average the theoretical resonance strengths agree to within .10% with experiment. The AUTOSTRUCTURE, MCDF, and R-matrix results are in better agreement with experiment than are the HULLAC results. However, in all cases the 1 � standard deviation for the ratios of the theoretical-to-experimental resonance strengths is &30%, which is significantly larger than the estimated relative experimental uncertainty of .10%. This suggests that similar errors exist in the calculated level populations and line emission spectrum of the recombined ion. We confirm that theoretical methods based on inverse-photoionization calculations (e.g., undamped R-matrix methods) will severely overestimate the strength of the DR process unless they include the effects of radiation damping. We also find that the coupling between the DR and radiative recombination (RR) channels is small. Below 2 eV the theoretical resonance energies can be up to � 30% larger than experiment. This is larger than the estimated uncertainty in the experimental energy scale (.0.5% below � 25 eV and .0.2% for higher energies) and is attributed to uncertainties in the calculations. These discrepancies makes DR of Fe xx an excellent case for testing atomic structure calculations of ions with partially filled shells. Above 2 eV, agreement between the theoretical and measured energies improves dramatically with the AUTOSTRUCTURE and MCDF results falling within 2% of experiment, the R-matrix results within 3%, and HULLAC within 5%. Agreement for all four calculations improves as the resonance energy increases. We have used our experimental and theoretical results to produce Maxwellian-averaged rate coefficients for DN ¼ 0D R of Fexx. For kBTe & 1 eV, which includes the predicted formation temperatures for Fe xx in an optically thin, low-density photoionized plasma with cosmic abundances, the experimental and theoretical results agree to better than � 15%. This is within the total estimated experimental uncertainty limits of .20%. Agreement below � 1 eV is difficult to quantify due to current theoretical and experimental limitations. Agreement with previously published LS-coupling rate coefficients is poor, particularly for kBTe . 80 eV. This is attributed to errors in the resonance energies of these calculations as well as the omission of DR via 2p1=2 ! 2p3=2 core excitations. We have also used our R-matrix results, topped off using AUTOSTRUCTURE for RR into J � 25 levels, to calculate the rate coefficient for RR of Fe xx. Our RR results are in good agreement with previously published calculations. We find that for temperatures as low as kBTe � 10 � 3 eV, DR still dominates over RR for this system. Subject headings: atomic data — atomic processes — methods: laboratory On-line material: machine-readable tables

Assessment of the fluorescence and auger database used in plasma modeling

We have investigated the accuracy of the 1s vacancy fluorescence database of Kaastra & Mewe resulting from the initial atomic physics calculations and the subsequent scaling along isoelectronic sequences. In particular, we have focused on the relatively simple Be- and F-like 1s vacancy sequences. We find that the earlier atomic physics calculations for the oscillator strengths and autoionization rates of singly charged B II and Ne II are in sufficient agreement with our present calculations. However, the substantial charge dependence of these quantities along each isoelectronic sequence, the incorrect configuration averaging used for B II, and the neglect of spin-orbit effects (which become important at high Z) all cast doubt on the reliability of the Kaastra & Mewe data for application to plasma modeling.