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All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Photoionization and Recombination

Theoretically self-consistent calculations for photoionization and (e + ion) recombination are described. The same eigenfunction expansion for the ion is employed in coupled channel calculations for both processes, thus ensuring consistency between cross sections and rates. The theoretical treatment of (e + ion) recombination subsumes both the non-resonant recombination ("radiative recombination"), and the resonant recombination ("di-electronic recombination") processes in a unified scheme. In addition to the total, unified recombination rates, level-specific recombination rates and photoionization cross sections are obtained for a large number of atomic levels. Both relativistic Breit-Pauli, and non-relativistic LS coupling, calculations are carried out in the close coupling approximation using the R-matrix method. Although the calculations are computationally intensive, they yield nearly all photoionization and recombination parameters needed for astrophysical photoionization models with higher precision than hitherto possible, estimated at about 10-20% from comparison with experimentally available data (including experimentally derived DR rates). Results are electronically available for over 40 atoms and ions. Photoionization and recombination of He-, and Li-like C and Fe are described for X-ray modeling. The unified method yields total and complete (e+ion) recombination rate coefficients, that can not otherwise be obtained theoretically or experimentally.

Nahar, Sultana N.↗
NASA NTRS1995

The FEM-R-Matrix Approach: Use of Mixed Finite Element and Gaussian Basis Sets for Electron Molecule Collisions

For the calculation of electron molecule collision cross sections R-matrix methods automatically take advantage of the division of configuration space into an inner region (I) bounded by radius tau b, where the scattered electron is within the molecular charge cloud and the system is described by an correlated Configuration Interaction (CI) treatment in close analogy to bound state calculations, and an outer region (II) where the scattered electron moves in the long-range multipole potential of the target and efficient analytic methods can be used for solving the asymptotic Schroedinger equation plus boundary conditions.

Thuemmel, Helmar T.↗
NASA NTRS2002

Photoionization of the Fe lons: Structure of the K-Edge

X-ray absorption and emission features arising from the inner-shell transitions in iron are of practical importance in astrophysics due to the Fe cosmic abundance and to the absence of traits from other elements in the nearby spectrum. As a result, the strengths and energies of such features can constrain the ionization stage, elemental abundance, and column density of the gas in the vicinity of the exotic cosmic objects, e.g. active galactic nuclei (AGN) and galactic black hole candidates. Although the observational technology in X-ray astronomy is still evolving and currently lacks high spectroscopic resolution, the astrophysical models have been based on atomic calculations that predict a sudden and high step-like increase of the cross section at the K-shell threshold (see for instance. New Breit-Pauli R-matrix calculations of the photoionization cross section of the ground states of Fe XVII in the region near the K threshold are presented. They strongly support the view that the previously assumed sharp edge behaviour is not correct. The latter has been caused by the neglect of spectator Auger channels in the decay of the resonances converging to the K threshold. These decay channels include the dominant KLL channels and give rise to constant widths (independent of n). As a consequence, these series display damped Lorentzian components that rapidly blend to impose continuity at threshold, thus reformatting the previously held picture of the edge. Apparent broadened iron edges detected in the spectra of AGN and galactic black hole candidates seem to indicate that these quantum effects may be at least partially responsible for the observed broadening.

Palmeri, P.↗
NASA NTRS2002

A Complete Set of Radiative and Auger Rates for K-vacancy States in Fe XVIII-Fe XXV

A complete set of level energies, wavelengths, A-values, and total and partial Auger rates have been computed for transitions involving the K-vacancy states within the n = 2 complex of Fe XVIII-Fe XXV. Three different standard numerical packages are used for this purpose, namely AUTOSTRUCTURE, the Breit-Pauli R-matrix suite (BPRM) and HFR, which allow reliable estimates of the physical effects involved and of the accuracy of the resulting data sets. It is found that the Breit interaction must be always taken into account as the contributions to the small A-values and partial Auger rates does not decrease with electron occupancy. Semi-empirical adjustments can also lead to large differences in both the radiative and Auger decay data of strongly mixed levels. Several experimental energy levels and wavelengths are questioned, and significant discrepancies are found with previously computed decay rates that are attributed to numerical problems. The statistical accuracy of the present level energies and wavelengths is ranked at plus or minus 3 eV and plus or minus 2 mAngstroms, respectively, whereas that for A-values and partial Auger rates greater than 10(exp 13) per second is estimated at better than 20%.

Palmeri, P.↗
NASA NTRS2003

Decay Properties of K-Vacancy States in Fe X-Fe XVII

We report extensive calculations of the decay properties of fine-structure K-vacancy levels in Fe X-Fe XVII. A large set of level energies, wavelengths, radiative and Auger rates, and fluorescence yields has been computed using three different standard atomic codes, namely Cowan's HFR, AUTOSTRUCTURE and the Breit-Pauli R-matrix package. This multi-code approach is used to the study the effects of core relaxation, configuration interaction and the Breit interaction, and enables the estimate of statistical accuracy ratings. The Ksigma and KLL Auger widths have been found to be nearly independent of both the outer-electron configuration and electron occupancy keeping a constant ratio of 1.53 +/- 0.06. By comparing with previous theoretical and measured wavelengths, the accuracy of the present set is determined to be within 2 m Angstrom. Also, the good agreement found between the different radiative and Auger data sets that have been computed allow us to propose with confidence an accuracy rating of 20% for the line fluorescence yields greater than 0.01. Emission and absorption spectral features are predicted finding good correlation with measurements in both laboratory and astrophysical plasmas.

Mendoza, C.↗
NASA NTRS2004

Electron-Hydrogen Elastic Scattering

Scattering by single-electron systems is always of interest because the wave function of the target is known exactly. Various approximations have been employed to take into account distortion produced in the target. Among them are the method of polarized orbitals and the close coupling approximation. Recently, e-H and e-He+ S-wave scattering in the elastic region has been studied using the Feshbach projection operator formalism. In this approach, the usual Hartree-Fock and exchange potentials are augmented by an optical potential and the resulting phase shifts have rigorous lower bounds. Now this method is being applied to the e-H P-wave scattering in the elastic region. The number of terms in the Hylleraas-type wave function for the 1,3 P phase shifts is 84 and the resulting phase shifts (preliminary) are given. The results have been given up to five digits because to that accuracy they are rigorous lower bounds. They are in general agreement with the variational (VAR) results of Armstead, and those obtained from the intermediate energy R-matrix method (RM) of Scholz et al., and the finite element method (FEM) of Botero and Shertzer. The later two methods do not provide any bounds on phase shifts.

Bhatia, A. K.↗
NASA NTRS2003

A Complete Set of Radiative and Auger Rates for K-vacancy States in Fe XVIII-Fe-XXV

A complete set of level energies, wavelengths, A-values, and total and partial Auger rates have been computed for transitions involving the K-vacancy states within the n = 2 complex of Fe XVIII-Fe XXV. Three different standard numerical packages are used for this purpose, namel y AUTOSTRUCTURE, the Breit-Pauli R-matrix suite (BPRM) and HFR, which allow reliable estimates of the physical effects involved and of the accuracy of the resulting data sets. The Breit interaction is taken i nto account because its contributions to the small A-values and partial Auger rates cannot be neglected with increasing electron occupancy. Semiempirical adjustments can also lead to large differences in both the radiative and Auger decay data of strongly mixed levels. Several experimental level energies and wavelengths are questioned, and significant discrepancies are found with previously computed decay rates th at are attributed to numerical problems. The statistical accuracy of the present level energies and wavelengths is ranked at +/-3 eV and +/ -2 mA, respectively, and that for A-values and partial Auger rates greater than lO(exp 13)/s at better than 20%.

Palmeri, P.↗
NASA NTRS1995

Electron Excitation Cross Sections for the C // Transitions 2s(sup 2)wp (sup 2)Pdegree -- 2s2p(sup 2) (sup 4)P, (sup 2)D and (sup 2)S

Experimental and theoretical excitation cross sections are reported for the transitions 2s22p 2Po 2s2p2 4P, 2D and 2S in C //. The transition wavelengths (energies) are l 2324 A (5.34 eV), l 1335 A (9.29 eV), and l 1036 A (11.96 eV), respectively. Use is made of electron energy-loss and merged- beams methods. The energy range covered is from below each threshold (4-11 eV) to 22-25 eV. As in previous work with O //, care was taken to assess and minimize the metastable fraction in the C //beam, to account for contributions from nearby energy-loss features, and to collect the full angular range of inelastically-scattered electrons. Comparison is made for each transition between experiment and a new 8-state R-matrix calculations.

Electron Excitation↗
NASA NTRS1994

Electron Excitation Cross Sections for the 2s(sup 2)2p(sup 3) (sup 4)S -> 2s(sup 2)2p(sup 3) (sup 2d) ->2s2p(sup 4) (sup 4p) (Resonance) Transitions in Oil

Experimental and theoretical excitation cross sections are reported for the first forbidden transition xxx and the first allowed (resonance) transition xxx in OII. Use is made of electron-energy loss and merged beams methods. The electron energy range covered is 3.33 eV (threshold) to 15 eV for the S->D transition, and 14.9 eV (threshold) to 40 eV for the S->P transition. Care was taken to assess and minimize the metastable fraction of the OII beam. An electron mirror was designed and tested to reflect inelastically back-scattered electrons into the forward direction to account for the full range of polar scattering angles. Comparisons are made between present experiments and 11-state R-Matrix calculations. Calculations are also presented for the xxx transition.

electron excitation↗
NASA NTRS2005

Measurement of absolute cross sections for excitation of the 2s(2) S-1 -> 2s2p P-1 degrees transition in O+4

Experimental cross sections are reported for the 1s(2)2s(2) S-1 -> 1s(2)2s2p P-1(o) transition in O+4 located at 19.689 eV. Use is made of the electron energy-loss method, using a merged electron-ion beam geometry. The center-of-mass interaction energies for the measurements in the S-1 -> P-1(o) transition are in the range 18 eV ( below the threshold) to 30 eV. Data are compared with other previous electron energy-loss measurements and with results of a 26 term R-matrix calculation that includes fine structure explicitly via the Breit-Pauli Hamiltonian. Clear resonance enhancement is observed in all experimental and theoretical results near the threshold for this S-1 -> P-1(o) transition.

atomic processes↗
NASA NTRS2006

Cross Sections for Electron Impact Excitation of Astrophysically Abundant Atoms and Ions

Electron collisional excitation rates and transition probabilities are important for computing electron temperatures and densities, ionization equilibria, and for deriving elemental abundances from emission lines formed in the collisional and photoionized astrophysical plasmas. Accurate representation of target wave functions that properly account for the important correlation and relaxation effects and inclusion of coupling effects including coupling to the continuum are essential components of a reliable collision calculation. Non-orthogonal orbitals technique in multiconfiguration Hartree-Fock approach is used to calculate oscillator strengths and transition probabilities. The effect of coupling to the continuum spectrum is included through the use of pseudostates which are chosen to account for most of the dipole polarizabilities of target states. The B-spline basis is used in the R-matrix approach to calculate electron excitation collision strengths and rates. Results for oscillator strengths and electron excitation collision strengths for transitions in N I, O I, O II, O IV, S X and Fe XIV have been produced

Tayal, S. S.↗
NASA NTRS2006

Low-Energy Elastic Electron Scattering by Atomic Oxygen

The B-spline R-matrix method is employed to investigate the low-energy elastic electron scattering by atomic oxygen. Flexible non-orthogonal sets of radial functions are used to construct the target description and to represent the scattering functions. A detailed investigation regarding the dependence of the predicted partial and total cross sections on the scattering model and the accuracy of the target description is presented. The predicted angle-integrated elastic cross sections are in good agreement with experiment, whereas significant discrepancies are found in the angle-differential elastic cross sections near the forward direction. .The near-threshold results are found to strongly depend on the treatment of inner-core short-range correlation effects in the target description, as well as on a proper account of the target polarizability. A sharp increase in the elastic cross sections below 1 eV found in some earlier calculations is judged to be an artifact of an unbalanced description of correlation in the N-electron target structure and the (N+l)-electron-collision problems.

Zatsarinny O.↗
NASA NTRS2007

Electron-Molecule Col1isions: Quantitative Approaches, and the Legacy of Aaron Temkin

This article, on electron-molecule collisions, is dedicated to the legacy of my good friend and sometime collaborator, Aaron Temkin on his retirement from the NASA-Goddard Space Flight Center after many years of work at the highest intellectual level in the theoretical treatment of electron-atom and electron-molecule scattering. Aaron's contributions to the manner in which we think about electron-molecule collisions is clear to all of us who have worked in this field. I doubt that the great progress that has occurred in the computational treatment of such complex collision problems could have happened without these contributions. For a brief historical account, see the discussion of Temkin's contribution to electron-molecule scattering in the first article of this volume by Dr. A. K. Bhatia. In this article, I will concentrate on the application of the so called, non-adiabatic R-matrix theory, to vibrational excitation and dissociative attachment, although I will also present some results applying the Linear Algebraic and Kohn-Variational methods to vibrational excitation. As a starting point for almost all computationally effective approaches to electron-molecule collisions, is the fixed nuclei approximation. That is, one recognizes, just as one does with molecular bound states, that there is a separation of electronic(fast) and nuclear(s1ow) degrees of freedom. This separation makes it possible to "freeze" the nuclei in space, calculate the collision parameters for the frozen molecule and then, somehow to add back the vibrations and rotations. The manner in which this is done, depends on the details of the collision problem. It is the work of Aaron and a number of other researchers that has provided the guidance necessary to resolve these issues.

Schneider, B.I.↗
NASA NTRS2007

Atomic Data and Spectral Line Intensities for CA XVII

Electron impact collision strengths, energy levels, oscillator strengths and spontaneous radiative decay rates are calculated for Ca XVII. The configurations used are 2s(sup 2), 2s2p, 2p(sup 2), 2l3l', 214l' and 2s5l', with l = s,p and l' = s,p, d giving rise to 92 fine-structure levels in intermediate coupling. Collision strengths are calculated at seven incident energies (15, 30, 75, 112.5, 150, 187.5 and 225 Ry) for the transitions within the three lowest configurations corresponding to the 10 lowest energy levels, and five incident energies (75, 112.5, 150, 187.5 and 225 Ry) for transitions between the lowest five levels and the n = 3,4,5 configurations. Calculations have been carried out using the distorted wave approximation. Excitation rate coefficients are calculated as a function of electron temperature by assuming a Maxwellian electron velocity distribution. Using the excitation rate coefficients and the radiative transition rates of the present work, and R-Matrix results for the 2s2, 2s2p, 2p2 configurations available in the literature, statistical equilibrium equations for level populations are solved at electron densities covering the range of 10(exp 8)-10(exp 14)/cu cm at an electron temperature of log Te(K)=6.7, corresponding to the maximum abundance of Ca XVII. Spectral line intensities are calculated, and their diagnostic relevance L; discussed. This dataset will be made available in the next version of the CHIANTI database.

Bhatia, A.K.↗
NASA NTRS2010

K-shell Photoionization of Na-like to Cl-like Ions of Mg, Si, S, Ar, and Ca

We present R-matrix calculations of photoabsorption and photoionization cross sections across the K edge of Mg, Si, S, Ar, and Ca ions with more than 10 electrons. The calculations include the effects of radiative and Auger damping by means of an optical potential. The wave functions are constructed from single-electron. orbital bases obtained using a Thomas-Fermi-Dirac statistical model potential. Configuration interaction is considered among all states up to n = 3. The damping processes affect the resonances converging to the K-thresholds causing them to display symmetric profiles of constant width that smear the otherwise sharp edge at the photoionization threshold. These data are important for the modeling of features found in photoionized plasmas.

Witthoeft, M. C.↗
NASA NTRS2013

A Comprehensive X-Ray Absorption Model for Atomic Oxygen

An analytical formula is developed to accurately represent the photoabsorption cross section of atomic Oxygen for all energies of interest in X-ray spectral modeling. In the vicinity of the K edge, a Rydberg series expression is used to fit R-matrix results, including important orbital relaxation effects, that accurately predict the absorption oscillator strengths below threshold and merge consistently and continuously to the above-threshold cross section. Further, minor adjustments are made to the threshold energies in order to reliably align the atomic Rydberg resonances after consideration of both experimental and observed line positions. At energies far below or above the K-edge region, the formulation is based on both outer- and inner-shell direct photoionization, including significant shake-up and shake-off processes that result in photoionization-excitation and double-photoionization contributions to the total cross section. The ultimate purpose for developing a definitive model for oxygen absorption is to resolve standing discrepancies between the astronomically observed and laboratory-measured line positions, and between the inferred atomic and molecular oxygen abundances in the interstellar medium from XSTAR and SPEX spectral models.

supernova remnants↗