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A&A
Volume 616, August 2018
Article Number A62
Number of page(s) 7
Section Atomic, molecular, and nuclear data
DOI https://doi.org/10.1051/0004-6361/201832939
Published online 17 August 2018

© ESO 2018

1. Introduction

Our project is concerned with the computation of atomic data to improve the diagnostic capabilities of the spectral K lines and edges of chemical elements with low cosmic abundance (trace elements), namely F, Na, P, Cl, K, Sc, Ti, V, Cr, Mn, Co, Cu, and Zn. In spite of their low abundances, they are nevertheless observed in the X-ray spectra of supernova remnants, galaxy clusters, and accreting black holes and neutron stars (see, e.g., Hwang et al. 2000; Miller et al. 2006; Badenes et al. 2008; Kallman et al. 2009; Tamura et al. 2009; Ueda et al. 2009; Nobukawa et al. 2010; Park et al. 2013), from which they can be used to constrain the plasma characteristics. For this purpose, level energies, radiative and Auger widths, and fluorescence yields for K-vacancy levels in ions of the isonuclear sequences described above were computed by Palmeri et al. (2012; hereafter PQM12) with HFR (a Hartree–Fock code with relativistic corrections by Cowan 1981). Their atomic target representations were subsequently used by Palmeri et al. (2016; hereafter Paper I) and Mendoza et al. (2017; hereafter Paper II) to calculate intermediate-coupling photoabsorption and photoionization cross sections for isoelectronic sequences with electron number N ≤ 18 with the Breit–Pauli R-matrix method (BPRM, Berrington et al. 1995). In this context, the resonance structures associated with the L and K ionization edges were studied in detail, particularly the radiative and spectator-Auger damping effects that lead to K-edge smearing (Palmeri et al. 2002).

In this final report of the project, we compute LS -coupling photoabsorption and photoionization cross sections for trace ions in isoelectronic sequences with 19 ≤ N ≤ 26 with the multi-purpose atomic structure code AUTOSTRUCTURE, assuming the isolated resonance approximation. This latter approach was adopted because BPRM has proven to be ineffective because the target sizes involved are too large. The accuracy of AUTOSTRUCTURE has previously been shown to be reasonable for this purpose (see Paper II), and is further examined here for the simpler K (N = 19) and Ca (N = 20) isoelectronic sequences.

An important part of this report is the curation aspects of the voluminous database that has been generated in this project (see Appendix A), which is to become available online from the CDS. We emphasize, however, that the datasets have been computed with different numerical methods and angular couplings, and their content and structures may thus vary nominally.

2. Numerical methods

The main task of this project is to compute photoabsorption and total and partial photoionization cross sections for ions of the isonuclear series P, Cl, K, Sc, Ti, V, Cr, Mn, Co, Cu, and Zn with electron numbers N < Z − 1, where Z is the atomic number identifying the sequence. As previously described in Paper I, species with Z − 1 ≤ N ≤ Z will be treated elsewhere. Cross sections for isoelectronic sequences with N ≤ 11 were reported in Paper I and with 12 ≤ N ≤ 18 in Paper II. We discuss here the details of the computations for fourth-row ions with 19 ≤ N ≤ 26.

The cross sections reported in Paper I and Paper II were carried out in intermediate coupling (IC) with the relativistic (Breit–Pauli) BPRM method, which allows the inclusion of radiative and spectator-Auger damping (Robicheaux et al. 1995; Gorczyca & Badnell 1996, 2000). The target representations listed in Table 9 of PQM12 were used, but for ions with 12 ≤ N ≤ 18, levels from the 2s-hole configurations [2s]μ were additionally included. Electronic orbitals were generated in a Thomas–Fermi–Dirac statistical potential with the AUTOSTRUCTURE atomic structure code (Eissner et al. 1974; Badnell 2011).

Because large target sizes are required for species with 19 ≤ N ≤ 26, especially those bearing ground configurations 3p63dm with m > 2, the BPRM approach is no longer practical. Exploratory calculations in Paper II revealed that LS cross sections could be adequately generated for such larger ions with a distorted-wave approach in the isolated-resonance approximation implemented in AUTOSTRUCTURE. Target models are still those from PQM12, but as previously shown (Paper II), they are complemented with levels from configurations of the type [2s]μ. Radiative damping is taken into account by AUTOSTRUCTURE, but in contrast to BPRM, the Auger decay branches must be explicitly specified in the configuration list, which leads to lengthy calculations. The key feature of this approach is the decoupling of the photoionization and photoexcitation processes that enables the treatment of larger systems.

3. Results

For the trace elements hardly any previous multichannel photoabsorption cross sections for fourth-row ions with ground configurations 3p63dm exist; therefore we calculated the cross sections from the ionization threshold up to the monotonic decreasing tail beyond the K edge. We illustrate the main findings of our analysis in terms of the Zn ions. For the potassium isoelectronic sequence (N = 19), it is still possible, although involved, to perform a BPRM calculation in IC to compare with AUTOSTRUCTURE. This comparison is carried out in Fig. 1 for the 3p63d 2D3/2 ground state of Zn XII, where the BPRM data below the L edge (~103 Ryd) have been convolved for clarity with a Gaussian of width ΔE/E = 0.001 (Fig. 1a). Salient spectral features in this region are the M edge (~30 Ryd) and the Lα transition array at ~82 Ryd, where resonance positions from the two numerical methods appear to agree adequately. Fig. 1b shows the near-K edge region above 720 Ryd, where the AUTOSTRUCTURE energy scale has been shifted by 0.9 Ryd to ensure resonance positional matching. This discrepancy is a direct consequence of adjusting the BPRM thresholds manually to the energy values listed in Table 9 of PQM12, a procedure that was performed throughout for all ions with electron number N ≤ 18. The broad dip at ~737 Ryd in the AUTOSTRUCTURE curve of Fig. 1b is a numerical artifact resulting from the finite number (n = 10) of K-vacancy states considered, and it illustrates the difficulties of rendering properly the region just below threshold.

thumbnail Fig. 1.

IC photoabsorption cross section of the 3p63d 2D3/2 ground state of K-like Zn XII computed with BPRM (black curve) and AUTOSTRUCTURE (red curve). Panel a: valence and L-edge regions; the BPRM cross section has been convolved with a Gaussian of width ΔE/E = 0.001. Panel b: K-edge region; the AUTOSTRUCTURE energy scale has been shifted by 0.9 Ryd to obtain resonance positional matching. C. Mendoza et al.: K-shell photoabsorption

A similar situation is found in a comparison between BPRM and AUTOSTRUCTURE in LS coupling for the 3p6 3d2 3F ground term of Ca-like Zn XI (Fig. 2). The positions of the AUTOSTRUCTURE L and M edges and the Lα transition array are somewhat lower (~2 Ryd) than BPRM (see Fig. 2a), while the K lines are ~1.5 Ryd higher (see Fig. 2b). Such differences are found to be typical and manageable, which is not the case if the non-fine structure relativistic corrections are neglected in AUTOSTRUCTURE, as shown in Fig. 2c, where now the discrepancies can be as large as 10 Ryd.

thumbnail Fig. 2.

LS -coupling photoabsorption cross section of the 3p63d23F ground state of Ca-like Zn XI computed with BPRM (black curve) and AUTOSTRUCTURE (red curve). Panel a: valence and L-edge regions; the BPRM cross section has been convolved with a Gaussian of width ΔE/E = 0.001. Panel b: K-edge region. Panel c: K-edge region where the AUTOSTRUCTURE cross section has been computed excluding the non-fine-structure relativistic corrections leading to a large positional discrepancy in the resonance structure.

In Fig. 3 we plot the photoabsorption cross sections of the Zn ions of the iron-group: Zn X (Sc-like), Zn IX (Ti-like), Zn VIII (V-like), Zn VII (Cr-like), Zn VI (Mn-like), and Zn V (Fe-like). The left panels show the region below 120 Ryd dominated by the L and M edges and the Lα transition arrays, while the right panels show the K edge and its associated damped lines, which are the spectral signatures of interest in X-ray astronomical spectra. An important issue here is how to improve the energy scale that is subject to the uncertainties in both the ionization potential and excitation thresholds. As shown by Gatuzz et al. (2013a, b) for the oxygen K lines, there are standing inconsistencies between the laboratory and observational energy scales that are deterrents in a reliable choice. As a consequence, no attempt is made here to adjust the energy scales.

thumbnail Fig. 3.

AUTOSTRUCTURELS photoabsorption cross sections of the ground states of Zn X (Sc-like), Zn IX (Ti-like), Zn VIII (V-like), Zn VII (Cr-like), Zn VI (Mn-like), and Zn V (Fe-like) in the valence and L-edge regions (left column) and K-edge region (right column).

4. Conclusions

Photoabsorption and photoionization cross sections have been computed for ions of the trace elements (elements with low cosmic abundance) F, Na, P, Cl, K, Sc, Ti, V, Cr, Mn, Co, Cu, and Zn with electron number N ≤ 26. Cross sections were computed in intermediate coupling with the Breit–Pauli R-matrix method BPRM for sequences with N ≤ 20; for the remaining sequences (21 ≤ N ≤ 26), they were obtained with AUTOSTRUCTURE in LS coupling because of the large target sizes, assuming the isolated resonance approximation. Comparisons between these two methods for K-like and Ca-like ions show that to ensure reasonable accuracy, it is vital to perform the LS calculations taking into account the non-fine-structure relativistic corrections. Curation procedures performed on the datasets stored at the CDS have been described to facilitate their download and use. These datasets will also be processed to be included in the atomic database of the XSTAR modeling code that calculates the physical conditions and emission spectra of photoionized gases (Bautista & Kallman 2001; Kallman et al. 2009).

As shown in Fig. 5b of Paper II, the BPRM photoabsorption cross section of Ar-like Sc iv in the K-edge region shows a small discontinuity at ≈331.5 Ryd where the optical potential associated with Auger damping is switched on. This feature will be found in most BPRM curves in the K-edge region. Similarly, the discontinuous AUTOSTRUCTURE cross section across the K-edge spectral head is due to the finite number of rendered resonances. This broad dip will be present in most of the cross sections computed with this code, as appreciated in Fig. 1b, Fig. 2b, c and Fig. 3 (right col.) of this report. Such numerical artifacts should be borne in mind.

There are hardly any previous calculations or experiments to reliably evaluate the accuracy of the present datasets. However, our target and collisional models have been extensively benchmarked with experiment and astronomical observations of K-line spectra involving ionic species from cosmic abundant isonuclear series, and in some cases, assessed by independent calculations with more refined approximations (e.g., the R-matrix plus pseudo-states framework). More precisely, we can cite the following sequences: N (García et al. 2009; Gharaibeh et al. 2011, 2014; Sant’Anna et al. 2011; Shorman et al. 2013); O (García et al. 2005, 2011; Gatuzz et al. 2013a, b, 2014; Gorczyca et al. 2013; McLaughlin et al. 2013a, b, 2014, 2017; Bizau et al. 2015); Ne, Mg, Si, S, Ar and Ca (Palmeri et al. 2008a; Witthoeft et al. 2011b); Al (Palmeri et al. 2011; Witthoeft et al. 2013) and Ni (Palmeri et al. 2008b; Witthoeft et al. 2011a).

The L-edge structure in ions with electron number N > 12, as discussed in Paper II, is not expected to be fully converged in contrast to that of the K edge. Moreover, as shown by Gorczyca et al. (2013) for O I, theoretical K resonance positions are always subject to small wavelength adjustments to fit astronomical or laboratory measurements, which for this specific system have been shown to be discrepant. These data sets should therefore be treated with due caution until they are independently verified.

Acknowledgments

This project is sponsored by NASA grant 12-APRA12-0070 through the Astrophysics Research and Analysis Program. PQ and PP are Research Director and Research Associate, respectively, of the Belgian Fund for Scientific Research F.R.S.-FNRS. We are indebted to Nigel Badnell (Strathclyde University, UK) for innumerable communications regarding the possibilities, features, and switches of the AUTOSTRUCTURE computer package.

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Appendix A

Database content and conventions

As previously described, the datasets generated in this project are to become available online from the CDS. We give here a concise description of the adopted data conventions and structures to identify the files and facilitate the extraction of their content.

A.1. Summary

Following the close-coupling (R-matrix) convention, where a scattering system is conceived as a target plus a colliding electron, we identify the N-electron ionic species to be photoionized with the 2-tuple (Z, NT), where Z is the atomic number and NT = N − 1 is the number of target electrons. In this project we have been mainly concerned with photoabsorption and photoionization cross sections of states in the ionic ground configuration that are referred to as photon states. They are identified by the 4-tuple (0, 2J, π, lev) in IC and (2S +1, L, π, lev) in LS , where J and L are the total and orbital angular momentum quantum numbers, respectively, 2S +1 the spin multiplicity, π the parity (π = 0 for even, π = 1 for odd), and lev the level index within the Jπ/S Lπ series. A summary of the database content in terms of these identifiers is given in Table A.1. It may be seen therein that 24 isoelectronic sequences with target electron numbers 2 ≤ NT ≤ 25 have been considered encompassing elements with atomic numbers 9 ≤ Z ≤ 30. Sequences with NT ≤ 19 have been treated in LS coupling, and for NT ≤ 20, Ni species have also been included to complement previous work by Witthoeft et al. (2011a).

Table A.1.

Summary of the ionic systems studied here identified by the 2-tuple (Z, NT), where Z is the atomic number and NT = N − 1 the number of target electrons.

A.2. Target data

IC energy-level data for (Z, NT) targets in isoelectronic sequences with 2 ≤ NT ≤ 18 and LS energy-level data for those with 19 ≤ NT ≤ 25 are listed in Tables A.2 and A.3, respectively. Energies in Rydbergs are given relative to the ground state, the latter listing the total ion energy. Table A.2 is very similar to Table 9 of PQM12, but since it is generated by BPRM-STG3, the level order may vary; moreover, for sequences with NT > 10, the level number is greater since additional configurations were taken into account. Tables A.2–A.3 are essential when considering the partial photoionization cross sections, which for a specific N-electron photon state are tabulated in i order.

Table A.2.

IC energy-level data for target ions (Z, NT) with NT ≤ 18.

Table A.3.

LS energy-level data for target ions (Z, NT) with 19 ≤ NT ≤ 25.

A.3. Photon-state data

The N-electron photon states for which cross sections have been computed are listed in Table A.4 (isoelectronic sequences with 3 ≤ N ≤ 19 in IC) and Table A.5 (sequences with 20 ≤ N ≤ 26, in LS); they essentially correspond to states within the ionic ground configuration. Energies are given in Rydbergs relative to the ionization potential. In systems with several photon states, IC cross sections for ions with N ≤ 19 are tabulated in i order.

Table A.4.

IC energy-level data for photon states of (Z, N) systems for which cross sections have been computed (N ≤ 19).

Table A.5.

LS energy-level data for photon states of the (Z, N) systems for which cross sections have been computed (20 ≤ N ≤ 26).

A.4. Photoabsorption and photoionization cross sections

Cross sections have been computed using the serial version of the Breit–Pauli R-matrix codes for isoelectronic sequences with target electron numbers NT ≤ 19 and with AUTOSTRUCTURE for 20 ≤ NT ≤ 25 (see Table A.1). Since the output files produced by these two suites of codes are somewhat different, we have kept the original nomenclature, structure, and formats rather than making an attempt to unify them. We have also avoided the conversion of cross sections computed in LS coupling to intermediate coupling. For an ionic species identified with the target tuple (Z, NT) ≡ (zz, nn), the following files have been included in the database.

For isoelectronic sequences with 2 ≤ NT ≤ 19,

  • zznn_xpatot: total photoabsorption cross sections.

  • zznn_xpisum: sum of the partial photoionization cross sections. It must be noted that this sum does not take into account the Auger-damped component since it is treated in BPRM by means of a model potential that does not specify parental branching.

  • zznn_xpipar: partial photoionization cross sections.

For isoelectronic sequences with 20 ≤ NT ≤ 25,

  • zznn_xpitot: total photoabsorption cross sections.

  • zznn_xdpisum: sum of the direct partial photoionization cross sections. It must be noted that in AUTOSTRUCTURE the direct photoionization and photoexcitation processes are computed separately, and for the larger ions with NT > 19, different target representations are implemented for each step that cannot be collated into a single unified target; therefore the resonance component is neglected.

  • zznn_xdpipar: direct partial photoionization cross sections.

All Tables

Table A.1.

Summary of the ionic systems studied here identified by the 2-tuple (Z, NT), where Z is the atomic number and NT = N − 1 the number of target electrons.

In the text
Table A.2.

IC energy-level data for target ions (Z, NT) with NT ≤ 18.

In the text
Table A.3.

LS energy-level data for target ions (Z, NT) with 19 ≤ NT ≤ 25.

In the text
Table A.4.

IC energy-level data for photon states of (Z, N) systems for which cross sections have been computed (N ≤ 19).

In the text
Table A.5.

LS energy-level data for photon states of the (Z, N) systems for which cross sections have been computed (20 ≤ N ≤ 26).

In the text

All Figures

thumbnail Fig. 1.

IC photoabsorption cross section of the 3p63d 2D3/2 ground state of K-like Zn XII computed with BPRM (black curve) and AUTOSTRUCTURE (red curve). Panel a: valence and L-edge regions; the BPRM cross section has been convolved with a Gaussian of width ΔE/E = 0.001. Panel b: K-edge region; the AUTOSTRUCTURE energy scale has been shifted by 0.9 Ryd to obtain resonance positional matching. C. Mendoza et al.: K-shell photoabsorption
In the text
thumbnail Fig. 2.

LS -coupling photoabsorption cross section of the 3p63d23F ground state of Ca-like Zn XI computed with BPRM (black curve) and AUTOSTRUCTURE (red curve). Panel a: valence and L-edge regions; the BPRM cross section has been convolved with a Gaussian of width ΔE/E = 0.001. Panel b: K-edge region. Panel c: K-edge region where the AUTOSTRUCTURE cross section has been computed excluding the non-fine-structure relativistic corrections leading to a large positional discrepancy in the resonance structure.
In the text
thumbnail Fig. 3.

AUTOSTRUCTURELS photoabsorption cross sections of the ground states of Zn X (Sc-like), Zn IX (Ti-like), Zn VIII (V-like), Zn VII (Cr-like), Zn VI (Mn-like), and Zn V (Fe-like) in the valence and L-edge regions (left column) and K-edge region (right column).
In the text

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