R-Matrix calculations for opacities: I. Methodology and computations

An extended version of the R-matrix methodology is presented for calculation of radiative parameters for improved plasma opacities. Contrast and comparisons with existing methods primarily relying on the Distorted Wave (DW) approximation are discussed to verify accuracy and resolve outstanding issues, particularly with reference to the Opacity Project (OP). Among the improvements incorporated are: (i) large-scale Breit-Pauli R-matrix (BPRM) calculations for complex atomic systems including fine structure, (ii) convergent close coupling wave function expansions for the (e+ion) system to compute oscillator strengths and photoionization cross sections, (iii) open and closed shell iron ions of interest in astrophysics and experiments, (iv) a treatment for plasma broadening of autoionizing resonances as function of energy-temperature-density dependent cross sections, (v) a "top-up" procedure to compare convergence with R-matrix calculations for highly excited levels, and (vi) spectroscopic identification of resonances and bound \eion levels. The present R-matrix monochromatic opacity spectra are fundamentally different from OP and lead to enhanced Rosseland and Planck mean opacities. An outline of the work reported in other papers in this series and those in progress is presented. Based on the present re-examination of the OP work, it is evident that opacities of heavy elements require revisions in high temperature-density plasma sources.Comment: 16 pages, 2 figure

A comprehensive set of UV and x-ray radiative transition rates for Fe XVI

Sodium-like Fe XVI is observed in collisionally ionized plasmas such as stellar coronae and coronal line regions of active galactic nuclei including black hole-accretion disc environments. Given its recombination edge from neon-like Fe XVII at ~25 Å, the Fe XVI bound-bound transitions lie in the soft x-ray and EUV (extreme ultraviolet) range. We present a comprehensive set of theoretical transition rates for radiative dipole allowed E1 transitions including fine structure for levels with nℓ(SLJ) ≤ 10, ℓ ≤ 9 using the relativistic Breit-Pauli R-matrix (BPRM) method. In addition, forbidden transitions of electric quadrupole (E2), electric octupole (E3), magnetic dipole (M1) and magnetic quadrupole (M2) type are presented for levels up to 5g(SLJ) from relativistic atomic structure calculations in the Breit-Pauli approximation using code SUPERSTRUCTURE. Some of the computed levels are autoionizing, and oscillator strengths among those are also provided. BPRM results have been benchmarked with the relativistic coupled cluster method and the atomic structure Dirac-Fock code GRASP. Levels computed with the electron collision BPRM codes in bound state mode were identified with a procedure based on the analysis of quantum defects and asymptotic wavefunctions. The total number of Fe XVI levels considered is 96, with 822 E1 transitions. Tabulated values are presented for the oscillator strengths f, line strengths S and Einstein radiative decay rates A. This extensive dataset should enable spectral modelings up to highly excited levels, including recombination-cascade matrices.This work was partially supported by the NASA Astronomy and Physics Research Program and the Astrophysical Theory Program. The computational work was carried out at the Ohio Supercomputer Center in Columbus, Ohio. CS acknowledges discussions with Professor B P Das, Professor D Mukherjee and Professor R K Chaudhuri

R-Matrix calculations for opacities.II. Photoionization and oscillator strengths of iron ions FeXVII, FeXVIII and FeXIX

Iron is the dominant heavy element that plays an important role in radiation transport in stellar interiors. Owing to its abundance and large number of bound levels and transitions, iron ions determine the opacity more than any other astrophysically abundant element. A few iron ions constitute the abundance and opacity of iron at the base of the convection zone (BCZ) at the boundary between the solar convection and radiative zones, and are the focus of the present study. Together, FeXVII, FeXVIII and FeXIX contribute 85\% of iron ion fractions 20\%, 39\% and 26\% respectively, at the BCZ physical conditions. We report heretofore the most extensive R-matrix atomic calculations for these ions for bound-bound and bound-free transitions, the two main processes of radiation absorption. We consider wavefunction expansions with 218 target or core ion fine structure levels of FeXVIII for FeXVII, 276 levels of FeXIX for FeXVIII, in the Breit-Pauli R-matrix (BPRM) approximation, and 180 LS terms (equivalent to 415 fine structure levels) of FeXX for FeXIX calculations. These large target expansions which includes core ion excitations to n=2,3,4 complexes enable accuracy and convergence of photoionization cross sections, as well as inclusion of high lying resonances. Photoionization cross sections have obtained for all bound fine structure levels of FeXVII and FeXVIII, and for 900 bound LS states of FeXIX. Selected results demonstrating prominent characteristic features of photoionization are presented, particularly the strong Seaton PEC (photoexcitation-of-core) resonances formed via high-lying core excitations with $\Delta n=1$ that significantly impact bound-free opacity.Comment: 22 pages, 10 figure

R-Matrix calculations for opacities: IV. Convergence, completeness, and comparison of relativistic R-matrix and distorted wave calculations for FeXVII and FeXVIII

To investigate the completeness of coupled channel (CC) Breit-Pauli R-Matrix (BPRM) calculations for opacities, we employ the relativistic distorted wave (RDW) method to complement (``top-up'') and compare the BPRM photoionization cross sections for high-$n\ell$ levels of both FeXVII and FeXVIII. Good agreement is found in background photoionization cross sections using these two methods, which also ensures correct matching of bound level cross sections for completeness. In order to top-up the CC-BPRM calculations, bound-bound transitions involving additional bound levels, and a large number of doubly-excited quasi-bound levels corresponding to BPRM autoionizing resonances described in paper RMOPII, are calculated using the RDW method. Photoionization cross sections in the high energy region are also computed and compared up to about 500 $Ry$, and contributions from higher core level excitations than BPRM are considered. The effect of configuration interaction is investigated, which plays a significant role in correctly reproducing some background cross sections. Owing to the fact that the additional RDW levels correspond to high-$n\ell$ bound levels that are negligibly populated according to the Mihalas-Hummer-D\"{a}ppen equation-of-state (Paper I), the effect on opacities is expected to be small.Comment: 15 pages, 6 figure

Relativistic photoionization cross sections for C II

High resolution measurements of photoionization cross sections for atomic ions are now being made on synchrotron radiation sources. The recent measurements by Kjeldsen etal. (1999) showed good agreement between the observed resonance features and the the theoretical calculations in the close coupling approximation (Nahar 1995). However, there were several observed resonances that were missing in the theoretical predictions. The earlier theoretical calculation was carried out in LS coupling where the relativistic effects were not included. Present work reports photoionization cross sections including the relativistic effects in Breit-Pauli R-matrix (BPRM) approximation. The configuration interaction eigenfunction expansion for the core ion C III consists of 20 fine structure levels dominated by the configurations from 1s^22s^2 to 1s^22s3d. Detailed features in the calculated cross sections exhibit the missing resonances due to fine structure. The results benchmark the accuracy of BPRM photoionization cross sections as needed for recent and ongoing experiments.Comment: 13 pages, 3 figure

Large-scale Breit-Pauli R-matrix calculations for transition probabilities of Fe V

Ab initio theoretical calculations are reported for the electric (E1) dipole allowed and intercombination fine structure transitions in Fe V using the Breit-Pauli R-matrix (BPRM) method. We obtain 3865 bound fine structure levels of Fe V and $1.46 x 10^6$ oscillator strengths, Einstein A-coefficients and line strengths. In addition to the relativistic effects, the intermediate coupling calculations include extensive electron correlation effects that represent the complex configuration interaction (CI). Fe V bound levels are obtained with angular and spin symmetries $SL\pi$ and $J\pi$ of the (e + Fe VI) system such that $2S+1$ = 5,3,1, $L \leq$ 10, $J \leq 8$. The bound levels are obtained as solutions of the Breit-Pauli (e + ion) Hamiltonian for each $J\pi$, and are designated according to the `collision' channel quantum numbers. A major task has been the identification of these large number of bound fine structure levels in terms of standard spectroscopic designations. A new scheme, based on the analysis of quantum defects and channel wavefunctions, has been developed. The identification scheme aims particularly to determine the completeness of the results in terms of all possible bound levels for applications to analysis of experimental measurements and plasma modeling. An uncertainty of 10-20% for most transitions is estimated.Comment: 31 pages, 1 figure, Physica Scripta (in press

Resonance structures in the multichannel quantum defect theory for the photofragmentation processes involving one closed and many open channels

The transformation introduced by Giusti-Suzor and Fano and extended by Lecomte and Ueda for the study of resonance structures in the multichannel quantum defect theory (MQDT) is used to reformulate MQDT into the forms having one-to-one correspondence with those in Fano's configuration mixing (CM) theory of resonance for the photofragmentation processes involving one closed and many open channels. The reformulation thus allows MQDT to have the full power of the CM theory, still keeping its own strengths such as the fundamental description of resonance phenomena without an assumption of the presence of a discrete state as in CM.Comment: 7 page

Irreducible tensor-form of the relativistic corrections to the M1 transition operator

The relativistic corrections to the magnetic dipole moment operator in the Pauli approximation were derived originally by Drake (Phys. Rev. A 3(1971)908). In the present paper, we derive their irreducible tensor-operator form to be used in atomic structure codes adopting the Fano-Racah-Wigner algebra for calculating its matrix elements.Comment: 26 page