Self-consistent R-matrix approach to photoionization and unified electron–ion recombination

Abstract

A unified scheme using the R-matrix method has been developed for electron-ion recombination subsuming heretofore separate treatments of radiative and dielectronic recombination (RR and DR). The ab initio approach within the coupled channel approximation has several inherent advantages in addition to the natural unification of resonant and non-resonant phenomena. It enables a general and self-consistent treatment of photoionization and electron-ion recombination employing idential wavefunction expansion. Detailed balance takes account of interference effects due to resonances in cross sections, calculated explicitly for a large number of recombined (e + ion) bound levels over extended energy regions. The theory of DR by Bell and Seaton is adapted for high-n resonances in the region below series limits. The R-matrix method is employed for (A) partial and total photoionization and photorecombination cross sections of (e + ion) bound levels, and (B) DR and (e + ion) scattering cross sections. Relativistic effects and fine structure are considered in the Breit-Pauli approximation. Effects such as radiation damping may be taken into account where necessary. Unfiied recombination cross sections are in excellent agreement with measurements on ion storage rings to about 10-20%. In addition to high accuracy, the strengths of the method are: (I) both total and level-specific cross sections and rate coefficients are obtained, and (II) a single (e + ion) recombination rate coefficient for any given atom or ion is obtained over the entire temperature range of practical importance in laboratory and astrophysical plasmas, (III) self-consistent results are obtained for the inverse processes of photoionization and recombination; comprehensive datasets have been computed for over 50 atoms and ions. Selected data are presented for iron ions.

Theoretical Fei–iiiEmission‐Line Strengths from Active Galactic Nuclei with Broad‐Line Regions

“…The IP data for collisions strengths for electron impact excitation were computed by Zhang & Pradhan (1995, hereafter IP.VI), for radiative transition probabilities, by Nahar (1995, hereafter IP.VII), and for photoionization cross sections, by Nahar & Pradhan (1994). We have adopted the smaller, 256 fine-structure level atom of Sigut & Pradhan (1998) for use in this calculation.…”

“…2), which include all Fe iii levels with known energies (see the NIST compilation; also Nahar & Pradhan 1996) We have used four principal sources to compile the required A ji -values for Fe iii transitions: the NIST critically evaluated database; the R-matrix results of Nahar & Pradhan (1996, hereafter IP.XVII) for dipole-allowed (ÁS ¼ 0) transitions 3 ; the Hartree-Fock calculations of Ekberg (1993), which also treats intersystem (ÁS 6 ¼ 0) transitions; and the extensive semiempirical calculations of Kurucz (1992).…”

“…3 Identification of the calculated (bound) Fe iii levels and their correspondence with the experimental NIST energy levels was performed by Nahar & Pradhan (1996) via the ELEVID code of Nahar (1995). 4 Turbulent velocity is used to refer to what is commonly denoted microturbulence by stellar astronomers; this velocity represents the width of a Gaussian distribution of turbulent motions small in scale compared to unit optical depth.…”

Resolution and accuracy of resonances in R-matrix cross sections

“…Accuracy of resonance positions is crucial in the determination of (e + ion) and photoionization rates. A number of self-consistent computations are in progress as part of a programme to calculate photoionization and unified (e + ion) recombination (RR plus DR) cross sections and rates (Nahar and Pradhan 2003a). 2.…”

“…Moreover, since the core ion is He-like, with a large radiative decay rate for the dominant core 1s2p( 1 P o 1 )→ 1s 2 ( 1 S 0 ) transition, radiation damping is important (Zhang et al 1999). This is particularly so in the calculation of unified photo-recombination rate coefficients for (e + O VII)↔O VI + hν (Nahar and Pradhan 2003b). The unified scheme to obtain total recombination rates, including RR and DR, entails: (A) highly resolved calculations of photoionization cross sections of a large number of bound levels, typically several hundred levels with effective quantum number ν ≤ 10 and (B) DR calculations using an adaptation of the theory by Bell and Seaton (1985), (Nahar and Pradhan 1994a) for 10 < ν ≤ ∞.…”