The Astrophysical Journal, 595:1307–1312, 2003 October 1 # 2003. The American Astronomical Society. All rights reserved. Printed in U.S.A.
INTERCHANNEL COUPLING IN IONIC PHOTOIONIZATION FAR ABOVE THRESHOLD: THE NEON ISOELECTRONIC SEQUENCE H. S. Chakraborty James R. Macdonald Laboratory, Department of Physics, Kansas State University, Manhattan, KS 66506-2601;
[email protected]
P. C. Deshmukh Department of Physics, Indian Institute of Technology-Madras, Chennai 600036, India;
[email protected]
and S. T. Manson Department of Physics and Astronomy, Georgia State University, Atlanta, GA 30303-3083;
[email protected] Received 2003 April 4; accepted 2003 June 6
ABSTRACT A study of the evolution of interchannel coupling in the photoionization of the Ne isoelectronic sequence from neutral Ne to Fe16+ has been performed. As in neutral Ne, the 2s cross section dominates the 2p at a high enough energy over the entire sequence and affects the 2p photoionization cross section via interchannel coupling. The importance of this coupling decreases gradually with increasing nuclear charge along the sequence. This has implications for databases of photoionization rates of astrophysical importance. Subject headings: atomic data — atomic processes
cross sections for atoms and ions, away from thresholds (Fano & Cooper 1968; Starace 1982; Amusia 1990). Recent experience, however, has shown that this conventional wisdom is not necessarily true (Dias et al. 1997; Hansen et al. 1999; Chakraborty et al. 2001). While IPA does a reasonably good job on the cross section for the dominant channel, the weaker channel cross sections can be considerably affected by interchannel coupling (Fano & Cooper 1968), which is essentially configuration interaction among continuum wave functions. Combined theoretical and experimental work for neutral atoms have shown that IPA breaks down in the 1 keV photon energy region for Ne (Dias et al. 1997), Ar (Hansen et al. 1999), and Kr (Chakraborty et al. 2001) photoionization, and this conclusion applies to both inner and outer shell photoionization. This is of particular importance in astrophysical modeling in which, as mentioned, much of the X-ray photoabsoption data are generated by IPA calculations (Reilman & Manson 1979; Verner & Yakovlev 1995). In the present paper, this idea is probed for ionic photoionization. Specifically, the Ne isoelectronic sequence is investigated from neutral Ne to Ne-like Fe, Fe16+, using the relativistic random phase approximation (RRPA) to treat the interchannel coupling (Johnson et al. 1980; Johnson & Cheng 1979).
1. INTRODUCTION
Photoinization of positive atomic ions is a fundamental process of nature. It is also of importance in a number of connections, particularly in diverse astrophysical and fusion plasmas (Arnaud & Rothenflug 1985; Arnaud & Raymond 1992; Kallman & Kahn 1996; Bottorff et al. 1998). In addition, the Chandra and XMM-Newton missions have enabled the detection of X-ray lines due to inner-shell photoabsorption, and these lines are ubiquitous in observations of active galactic nuclei outflows and the neutral interstellar medium (Behar & Kahn 2002). Photoabsorption of inner-shell resonance lines has also recently been shown to be an important process in these regions (Behar & Netzer 2002). Interpretation of this data requires an accurate knowledge of the relevant X-ray photoionization cross sections. Moreover, the interpretation of the data contributes to the understanding of the central regions of the first galaxies and their effect on the chemical enrichment of the universe (Ferland & Schultz 2002). In addition, experimental technology has improved to the point that the combination of third-generation light sources, along with the new ion sources, has made the experimental study of ionic photoionization feasible for some of the ions of astrophysical interest (Schlachter & Wuilleumier 1992; Wuilleumier & West 1996). However, experimental data will never be extensive enough to supply all of the photoabsorption cross sections (rates) required by the astrophysical community. Thus, theoretical predictions for cross sections are needed. At low photon energies, there exists a fair bit of theoretical data, notably from the Opacity and Iron Projects and their successors (Mendoza 1996; Hummer et al. 1993; Nahar 2000) for astrophysically abundant ions. At the higher energies, far less theoretical data exist, and the bulk of that data result from simple independent particle approximation (IPA) calculations (Reilman & Manson 1979; Verner & Yakovlev 1995); IPA was long thought to be entirely adequate for the calculation of photoionization
2. BRIEF REVIEW OF THEORY
The photoionization channels considered in this study are 2p3=2 2p1=2
! d5=2 ; d3=2 ; s1=2 ; ! d3=2 ; s1=2 ;
2s1=2 1s1=2
! !
p3=2 ; p1=2 ; p3=2 ; p1=2 :
These nine relativistic channels represent all of the single electron excitations from the ground state of Ne-like systems. Briefly, the RRPA calculation starts with the 1307
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Dirac-Fock (DF) single-particle wave functions for each subshell of the initial (ground) state of the Ne-like system. Then the RRPA equations, one for each of the relativistic channels listed above, are solved iteratively starting with the DF functions as an initial approximation. The converged RPPA solutions to these equations are then used to calculate the photoionizing transition matrix elements and thus the cross sections. The theoretical methodology is given in full detail elsewhere (Johnson et al. 1980; Johnson & Cheng 1979). Note that the RRPA formalism includes significant (but not all) aspects of electron-electron correlation. Of importance for the present calculation is that RRPA includes interchannel coupling among all single excitation channels, as well as discrete state correlation in the form of configuration interaction with all single and double promotions. These are expected to be the dominant correlations at the higher energies (Dias et al. 1997; Hansen et al. 1999; Chakraborty et al. 2001). A previous calculation on neutral Ne using this same methodology showed excellent agreement with the experiment (Dias et al. 1997); the quality of the calculations of the photoionization cross section for Ne-like ions should be at least as good, or better, since the interelectron interactions, the interactions that result in the correlation that theoretical atomic calculations approximate, become less and less important with increasing nuclear charge Z. To see this clearly, note that the (nonrelativistic) Hamiltonian for an N-electron ion of nuclear charge Z is given by N 2 X pi Ze2 H¼ 2m ri i¼1 ! N N N N X X e2 X p2i e2 1 X e2 Z þ ¼ : ð1Þ r 2m ri Z i
