Free Access
Issue
A&A
Volume 541, May 2012
Article Number A90
Number of page(s) 10
Section Atomic, molecular, and nuclear data
DOI https://doi.org/10.1051/0004-6361/201118720
Published online 04 May 2012

© ESO, 2012

1. Introduction

The soft X-ray (50–170 Å) spectrum of the quiet and active Sun is rich in n = 4 → n = 3 transitions from highly ionised iron ions, from Fe vii to Fe xvi (see, e.g. Fawcett et al. 1968). Very little atomic data are currently available for these ions and the majority of the spectral lines still await firm identification. Soft X-ray spectra of stellar coronae are routinely observed with the Chandra Low Energy Transmission Grating spectrometer (LETG, see Brinkman et al. 2000).

The Solar Dynamic Observatory (SDO) Extreme ultraviolet Variability Experiment (EVE) (Woods et al. 2010) has also been providing soft X-ray spectra. The SDO Atmospheric Imaging Assembly (AIA, see Lemen et al. 2011) has been observing (for the first time routinely) the solar corona in two broad-bands (among others) centred in the soft X-rays, around 94 and 131 Å. These SDO/AIA observations provide unprecedented coverage in terms of spatial and temporal resolutions, and can provide new diagnostic applications, once the atomic data are well understood. As shown in O’Dwyer et al. (2010) and Del Zanna et al. (2011), these bands are dominated by Fe x and Fe viii in normal quiet Sun conditions. However, several unidentified spectral lines have been observed in the AIA passbands with high-resolution grazing incidence solar spectrometers (cf. Behring et al. 1976; Manson 1972).

The atomic data for Fe viii and Fe ix relevant for the soft X-rays have recently been discussed in O’Dwyer et al. (2012), where new distorted wave (DW) scattering calculations for these two ions were presented.

This paper focuses on the atomic data for the Fe x n = 4 → n = 3 transitions. One of the main transitions is centred at 94 Å and is expected to provide the dominant signal to the SDO/AIA 94 Å band in quiet Sun conditions. Large discrepancies (a factor of six) between predicted and observed count rates in this band have been reported (cf. Aschwanden & Boerner 2011), which could in part be ascribed to problems in the atomic data for Fe x. Indeed, as shown by Malinovsky et al. (1980), large (at least a factor of two) discrepancies between predicted and observed intensities have been found to be present for all the 3s23p4 4s decays to the ground state.

We set out to resolve these discrepancies with a new set of calculations. We encountered along the way a series of problems and issues with the atomic physics model which turn out to be quite general and very interesting.

These Fe x transitions are of particular significance for the history of the solar corona. In fact, the famous first identification of a coronal line was given by Edlén (1942) (upon suggestion from Grotrian 1939) as the Fe x forbidden 2P3/22P1/2 transition within the ground configuration. Grotrian’s suggestion was based on the pioneering laboratory work by Edlén in the 1930’s on the identifications of the soft X-ray lines, in particular the Fe x 3s23p4 4s decays to the ground (Edlén 1937).

The paper is organised as follows. In Sect. 2, we give a brief review of previous soft X-ray observations and atomic calculations. In Sect. 3 we outline the methods we adopted for the scattering calculations. In Sect. 4 we present our results and in Sect. 5 we reach our conclusions with respect to Fe x and other ions.

2. Previous observations and atomic data for Fe x

A detailed discussion of the identifications, the historical context, and the atomic data for the n = 2,3 configurations, giving rise to spectral lines from the EUV to the visible was presented in Del Zanna et al. (2004) and is not repeated here. Del Zanna et al. (2004) presented new identifications and a set of new observed energies that are adopted here. The energies of the 3s23p43d levels have all been confirmed with recent, accurate EUV observations with the Hinode EUV Imaging Spectrometer (Del Zanna 2012).

For the soft X-rays (n = 4 → n = 3 transitions), Edlén carried out the first work on the identification of some 3s23p4 4s decays to the ground. This was followed by the monumental work by Fawcett et al. (1972), where a number of lines arising from the 3s23p4 4l (l =  s, p, d, f) levels were identified. It is important to keep in mind that only lines with strong oscillator strengths were identified, that some identifications were tentative, and that a large number of lines in the laboratory spectra were left unidentified. Not all of Fawcett’s work has been adopted within the NIST compilation.

We have re-analysed some of Fawcett’s plates as part of a larger project to sort out the identifications in the Fe soft X-ray spectrum. We have also considered various other experimental sources, in particular the excellent (still the best) grazing-incidence spectra of the full Sun taken in the late 1960s during rocket flights (see Manson 1972; Behring et al. 1972; Malinovsky & Heroux 1973). Virtually all spectral lines, even at high resolution, are blended. The majority of lines are still unidentified and very few reliable atomic data are available. For these reasons, a full comparison and benchmarking with observations is deferred to a future paper.

The first comprehensive collision strength calculation for Fe x was published by Mason (1975). She used the University College London (UCL) distorted-wave DW code (Eissner 1998), which includes the superstructure program (Eissner et al. 1974). Only the lowest 3s2 3p5, 3s 3p6, and 3s2 3p4 3d configurations were included.

Malinovsky et al. (1980) also used the UCL-DW code to calculate collision strengths, but this time for the n = 4 levels. The authors focused on the 3s23p4 4s decays to the ground. Large (factors of 5 to 6) discrepancies between the observed (by Malinovsky & Heroux 1973) and calculated line intensities were found. Cascading from higher levels was found to be important, but difficult to estimate. The inclusion of cascading contributions improved the comparison, but still left discrepancies of a factor of two or more. To our knowledge, no other calculations for the n = 4 levels have been published since.

For the n = 3 levels there are a number of calculations. Pelan & Berrington (2001) published, as part of the Iron Project, a full Breit-Pauli R-matrix calculation for a target including 180 levels arising from the five lowest n = 3 configurations. Collision strengths were calculated for a total of 7460 energy points in the resonance region (up to 9.95 Ryd). Pelan & Berrington (2001) only published excitation data from the three levels arising from 3s2 3p5, 3s 3p6. Given that there are a number of metastable states for this ion, collision data from those states are also needed (Del Zanna et al. 2004). Hence, a new calculation was needed. In addition, the “top-up” procedure was not applied in Pelan & Berrington (2001), and collision strengths for the strongest lines were found to be inaccurate (see Aggarwal & Keenan 2005).

Del Zanna et al. (2004) repeated the earlier Pelan & Berrington (2001) calculation for the lowest 31 levels due to the 3s2 3p5, 3s 3p6, and 3s2 3p4 3d configurations but with the addition of high partial wave top-up. These latter data have been used since 2005 within the CHIANTI database (Dere et al. 1997; Landi et al. 2006). Good overall agreement between predicted and observed line intensities using these atomic data was found in Del Zanna et al. (2004) and later in Del Zanna (2012).

Aggarwal & Keenan (2005) later performed a Dirac Atomic R-matrix Code (DARC) calculation for the lowest 90 levels of the 3s2 3p5, 3s 3p6, and 3s2 3p4 3d, 3s 3p5 3d, 3s2 3p3 3d2 configurations. This calculation was in some respects quite similar to Pelan & Berrington (2001). However, large differences (up to a factor of two) were found for some allowed transitions such as the 1–3. Relatively good agreement between the Aggarwal & Keenan (2005) and Del Zanna et al. (2004) is found however, as shown below.

Table 1

List of a few among the strongest Fe x lines in the soft X-rays.

3. Methods

The atomic structure calculations were carried out using the autostructure program (Badnell 1997) which constructs target wavefunctions using radial wavefunctions calculated in a scaled Thomas-Fermi-Dirac statistical model potential with a set of scaling parameters.

The Breit-Pauli distorted wave calculations were carried out using the recent development of the autostructure code, described in detail in Badnell (2011). The continuum distorted waves are calculated using the same form for the distorting potential as specified for the target, but now for the (N + 1)-electron problem. The electrostatic (N + 1)-electron interaction Hamiltonian for the collision problem is determined in an unmixed LS-coupling representation. It is then transformed to an LSJ representation. The full (N + 1)-electron interaction Hamiltonian is transformed to a full Breit-Pauli jK-coupling representation (i.e. including both configuration and fine-structure target mixing) in the same manner as is done for the (inner-region) Breit-Pauli R-matrix method. Collision strengths are calculated at the same set of final scattered energies for all transitions. “Top-up” for the contribution of high partial waves is done using the same Breit-Pauli methods and subroutines implemented in the R-matrix outer-region code STGF. The program also provides radiative rates and infinite energy Born limits. These limits are particularly important for two aspects. First, they allow a consistency check of the collision strengths in the scaled Burgess & Tully (1992) domain (see also Burgess et al. 1997). Second, they are used in the interpolation of the collision strengths at high energies when calculating the Maxwellian averages.

The R-matrix method used in the scattering calculation is described in Hummer et al. (1993) and Berrington et al. (1995). We performed the calculation in the inner region in LS coupling and included mass and Darwin relativistic energy corrections.

The outer region calculation used the intermediate-coupling frame transformation method (ICFT) described by Griffin et al. (1998), in which the transformation of the multi-channel quantum defect theory unphysical K-matrix to intermediate coupling uses the so-called term-coupling coefficients (TCCs) in conjunction with level energies.

Dipole-allowed transitions were topped-up to infinite partial wave using an intermediate coupling version of the Coulomb-Bethe method as described by Burgess (1974) while non-dipole allowed transitions were topped-up assuming that the collision strengths form a geometric progression in J (see Badnell & Griffin 2001).

The collision strengths were extended to high energies by interpolation using the appropriate high-energy limits in the Burgess & Tully (1992) scaled domain. The high-energy limits were calculated with autostructure for both optically-allowed (see Burgess et al. 1997) and non-dipole allowed transitions (see Chidichimo et al. 2003). All the transitions from the ground configuration were visually inspected. General agreement in the background collision strengths was found with the DW values, and at high energies with the limit points.

The temperature-dependent effective collisions strength Υ(i − j) were calculated by assuming a Maxwellian electron distribution and linear integration with the final energy of the colliding electron.

4. Results

Several calculations have been performed with different size target expansions and corresponding ion population models have been constructed to predict line intensities and compare with observations. A summary of our investigations is presented here.

4.1. Initial DW calculations

We started with various DW calculations systematically increasing the number of configurations up to and including those with n = 6 valence orbitals. As shown by Del Zanna et al. (2004), a number of metastable levels within the 3s2 3p4 3d configuration become significantly populated at coronal densities (up to level 24). Hence, DW excitation rates from the lowest 24 levels have been calculated.

We then performed separate structure calculations for each ion model to calculate all of the radiative data for all transitions among the levels. This ensures that all the cascading from the target configurations is included. We then calculated the level populations and the relative line intensities so as to find out which lines are expected to be strongest in quiet Sun conditions.

Following Malinovsky et al. (1980), the intensities of the soft X-ray lines (4s–3p) have been considered relative to the strongest EUV line (3d–3p). Table 1 shows the details for a few transitions among the strongest lines from the main n = 4 configurations. The relative intensities obtained from two purely DW runs, which are described below, are displayed in the first two intensity columns of Table 1. The first DW ion model includes almost all possible of the n = 3,4 configurations. The second DW ion model also includes the main n = 5,6 configurations. The other ion models we built produce similar results. The following two columns show the results obtained with the models described below, while the last one shows the values calculated with the current CHIANTI model, which has the Malinovsky et al. (1980) collisional data.

One of the strongest lines in the soft X-rays is the 3s2 3p5 2P3/2–3s2 3p4 4s 2D5/2 identified by Edlén (1937) at 94.012 Å. The relative intensity with the n = 4 DW model is 5.3 × 10-3 (in photons), i.e. almost six times weaker than observed (3.2 × 10-2) by Malinovsky & Heroux (1973) and about a factor of two lower than calculated by Malinovsky et al. (1980) (1.0 × 10-2). As shown by Malinovsky et al. (1980), cascading from higher levels does increase the population of the 4s 2D5/2, but only at the 10−20% level. Our large n = 6 DW model predicts a relative intensity of 7.5 × 10-3, larger as expected, but also lower than the value calculated by Malinovsky et al. (1980) (1.2 × 10-2).

Similar discrepancies between Malinovsky et al. (1980) and our results are present for the other lines in the same transition array. The differences between our results and Malinovsky et al. (1980) in the calculated values should not be present since very similar (DW) scattering approximations have been used. Actually, for dipole-allowed lines, Malinovsky et al. (1980) only calculated DW collision strengths at 12 and 20 Ryd, while a semi-classical approximation, based on Burgess (1964), was used at 40 and 80 Ryd. It is not entirely clear which set of configurations was used by Malinovsky et al. (1980). However, we have run a DW calculation including the same set of configurations as listed in their paper, and the differences remain. It turns out that the differences are due to significantly overestimated collision strengths by Malinovsky et al. (1980), as shown below.

The overestimation of collision strengths by Malinovsky et al. (1980) only makes the problem worse in terms of comparison with solar data. The cause could in part be due to an incorrect photometric calibration of the Malinovsky & Heroux (1973) spectrum in the soft X-rays. A discussion of this is deferred to a future paper. However, even just considering the soft X-rays, significant problems are still present. In particular, the DW calculations clearly indicate that the 3s 3p6 2S1/2 − 3s 3p5 4s 2P3/2 transition is almost three times stronger than the 3s2 3p5 2P3/2 − 3s2 3p4 4s 2D5/2 94 Å line. This is caused by a strong forbidden excitation from the ground state to the 3s 3p5 4s 2P3/2, with collision strengths much higher than those to the 3s2 3p4 4s levels, as discussed below. The 3s 3p5 4s 2P3/2 level then decays via a strong dipole-allowed transition. This transition has not been identified previously. However, our ab-initio calculations predict this line to fall around 95−96 Å. At around these wavelengths there are no lines in the solar spectrum which are two or three times stronger than the 94 Å line. The same holds for the laboratory plates from Fawcett which we have analysed.

All of the DW calculations we have carried out produced similar values. We have also run similar calculations for other iron ions and found the same situation: strong transitions from 3s 3pq 4s, not identified by Edlén or Fawcett. In general, we have found significant numbers of unidentified lines, stronger than those that have been identified, which complicates the benchmarking of the atomic data. As stated previously, a full discussion of benchmarking with solar and laboratory spectra is beyond the scope of this paper and is deferred to a future paper.

The only reasonable solution to the problem is that all of the excitations to the 3s2 3p4 4s levels are significantly underestimated by the DW calculations. Indeed, we previously found a similar situation for Fe ix, as discussed in O’Dwyer et al. (2012). We found that there are resonances which increase significantly the collision strengths to the 3s2 3p5 4s levels. A purely (non-resonant) DW calculation would underestimate by at least a factor of two the intensities of any decays from these levels, compared to what is obtained with an R-matrix calculation (Storey et al. 2002).

4.2. Estimate of resonance contribution

A full R-matrix calculation with n = 4,5 levels is challenging, so before embarking on such a calculation we performed various DW calculations to estimate which configurations would be likely to be producing resonances in the collision strengths for the spectroscopically important configurations/levels. For each model, we calculated all the collision strengths at threshold between all the levels. The details of two of such calculations are given below. Here, we are using results form the larger of the two calculations.

To assess which configurations would contribute significantly, we considered two steps, the first being dielectronic capture which is directly proportional to the excitation collision strengths. Only levels with similar excitations from the ground configuration can be important. The second step is the Auger decay, which has a rate proportional to the excitation cross-section between the levels (Burgess 1965). If we identify all first step excitations that are stronger or comparable with the direct excitations of interest then we necessarily have all possible candidates for strong resonance contributions. Whether these do in fact contribute strongly, depends on step two.

thumbnail Fig. 1

The main levels related to the 3s2 3p4 4s 2D5/2, which produces the 94.012 Å line. The values of the collision strengths at threshold among the levels and from the ground state are shown.

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thumbnail Fig. 2

The term energies of the target levels (32 configurations) for the n = 4 calculations. The 218 terms which produce levels having energies below the dashed line have been retained for the close-coupling expansion.

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Consider as an example the 3s2 3p4 4s 2D5/2 level which is populated by a dipole excitation from the ground state but with the relatively small threshold collision strength of 0.027 (see Fig. 1). The collision strength for the dipole forbidden excitation of the 3s2 3p4 4p 2P3/2 from the ground state, on the other hand is large, 0.6 at threshold, implying a large dielectronic capture rate to the resonances converging on this state. These resonances can autoionize into all possible open channels but the DW calculations show that the two main routes leave the ion either in its ground state or in the 3s2 3p4 4s 2D5/2 level. The threshold collision strengths, 0.6 and 2.1 respectively, provide an estimate of the branching ratio between these routes, with 80% leaving the ion in the 3s2 3p4 4s 2D5/2 level. Since the average effect of the resonances converging on the 3s2 3p4 4p 2P3/2 can be thought of as an extrapolation of the threshold collision strength to negative final energy, this implies that the collision strength for excitation to the 3s2 3p4 4s 2D5/2 level will be enhanced by 0.48 in the energy interval between the 3s2 3p4 4s 2D5/2 and 3s2 3p4 4p 2P3/2 levels, almost 20 times the value for direct excitation. We will show below that the result of a detailed R-matrix treatment of the resonances gives a similar increase. These are estimates based on total threshold collision strengths. A full treatment involves detailed consideration of all the scattering channels (see, e.g. Petrini 1970).

Other contributions could also come from other configurations connected to the 3s2 3p4 4s by a dipole coupling, such as 3s2 3p3 3d 4s, 3s 3p5 4s and 3s2 3p4 np, n ≥ 5. The latter configurations are especially interesting given the large contribution from n = 4. In practice we do not find large collision strengths for excitation of the 3s2 3p4 np for n = 5,6 from the ground and also there are additional Auger channels reducing the branching ratio to the 3s2 3p4 4s levels.

We used the same approach to assess the importance of resonance contributions to the other levels of the n = 4,5 configurations. We found that the 3s 3p5 4s levels are not expected to have significant contributions from resonances. The 3s2 3p4 4p levels have significant resonance contributions, mainly from the 3s2 3p4 4d, 3s2 3p4 4f and 3s2 3p3 3d2. The 3s2 3p4 4d levels are expected to have some contributions, mainly from the 3s2 3p4 4f. On the other hand, the 3s2 3p4 4f levels are not expected to have significant resonance contributions from other n = 4,5 levels. A similar picture applies to the n = 5 levels.

In summary, with the exception of a small contribution from the 3s2 3p4 5p levels to the 3s2 3p4 4s (and 3s2 3p4 4p), the main resonance contribution to the n = 4 spectroscopic configurations comes from configurations within the n = 4 complex. We have therefore chosen to proceed with a full R-matrix calculation including all the main n = 3,4 configurations.

Table 2

The target electron configuration basis and orbital scaling parameters λnl for the R-matrix and DW runs for the n = 3,4 levels.

4.3. The R-matrix and DW calculations for the n = 3,4 levels

As our configuration basis set we have chosen the 32 configurations shown in Fig. 2 and listed in Table 2. The scaling parameters λnl for the potentials in which the orbital functions are calculated are also given in Table 2. The 552 fine-structure levels arising from the lowest 218 LS terms were retained for the scattering calculation. We have performed both an ICFT R-matrix and a DW calculation using the same basis. They are both large-scale calculations.

Table 3

Level energies for Fe x (n = 3,4).

Table 3 presents a selection of fine-structure target level energies Et, compared to experimental energies Eexp (from Del Zanna et al. 2004, for the n = 3 levels; otherwise from Fawcett et al. 1972). There is good overall agreement in terms of energy differences between levels. A set of “best” energies Eb was obtained with a quadratic fit between the Eexp and Et values. The Eb values were used (together with the Eexp ones) within the R-matrix calculation to obtain an accurate position of the resonance thresholds. The resonances in the transitions to the n = 4 levels are close to thresholds, therefore it is important to position them as accurately as possible. The Eexp and Eb values were also used when calculating radiative rates.

The expansion of each scattered electron partial wave was done over a basis of 25 functions within the R-matrix boundary and the partial wave expansion extended to a maximum total orbital angular momentum quantum number of L = 16. This produced accurate collision strengths up to about 80 Ryd. The resulting effective collision strengths are accurate up to an electron temperature of about 107 K. However, the interpolation for all allowed transitions utilizing the infinite limits makes the data reliable at even greater temperatures. (The collision strengths for forbidden transitions are extrapolated as 1/E2.)

The outer region calculation includes exchange up to a total angular momentum quantum number J = 26/2. We have supplemented the exchange contributions with a non-exchange calculation extending from J = 28/2 to J = 74/2. The outer region exchange calculation was performed in a number of stages. A coarse energy mesh was chosen above all resonances. The resonance region itself was calculated with an increasing number of energies, as was done for the Iron Project Fe xi calculation (Del Zanna et al. 2010). Pelan & Berrington (2001) suggested that a step in energy between 0.001 and 0.002 Ryd was sufficient to resolve the resonances. Here, the number of energy points was increased from 2000 up to 8000 (equivalent to a uniform step length of 0.0018 Ryd). We have then considered all the transitions from the ground state and calculated the maximum deviation between the various calculations of the thermally-averaged collision strength. The results are shown in Fig. 3.

thumbnail Fig. 3

Maximum relative difference (in percentage) between the thermally-averaged collision strengths from the ground state, calculated with an increasing number of energy points, from 2000 to 8000.

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thumbnail Fig. 4

Above: collision strength for the forbidden red coronal line, averaged over 0.1 Ryd in the resonance region. The data points are displayed in histogram mode. Boxes indicate the DW values. Below: thermally-averaged collision strengths, with other calculations.

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thumbnail Fig. 5

Same as Fig. 4, for the allowed 1−3 345.74 Å transition.

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thumbnail Fig. 6

Same as Fig. 4, for the strong forbidden 1–5 257.26 Å transition.

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thumbnail Fig. 7

Same as Fig. 4, for the allowed 1–30 174.53 Å transition, the strongest in the EUV.

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We then inspected all transitions from the ground state, and compared the collision strengths and their thermal averages with other datasets. The comparisons for a selection of levels giving rise to important transitions are displayed in Figs. 412. Excellent agreement between the background R-matrix and the DW collision strengths is found in all cases. This is to be expected since they both use the same target. For the main n = 3 transitions, good overall agreement with Aggarwal & Keenan (2005) and Del Zanna et al. (2004) is found. Interestingly, the 1−5 transition has considerably larger collision strengths than what was calculated by Del Zanna et al. (2004). The latter atomic data were used in Del Zanna (2012) where it was found that the intensity of the 1−5 line was underestimated by about 50%. The new atomic data remove the discrepancy.

Figure 8 shows the collision strengths for the 94.012 Å transition. A strong enhancement due to resonances is present, of the same order as predicted using the approximate method of Sect. 4.2. This produces an increase of about a factor of two in the rate (and, hence, line intensities) at coronal (1 MK) temperatures. The asterisks are the Malinovsky et al. (1980) calculations, DW at 12 and 20 Ryd and semi-classical at 40 and 80 Ryd. It is clear that Malinovsky et al. (1980) overestimated the second pair of collision strengths. This produces around a factor of two increase in the rates (and, hence, line intensities) at coronal temperatures. All other lines from the same transition array show a similar behaviour.

thumbnail Fig. 8

Same as Fig. 4, for the allowed 94.012 Å transition. Note the strong enhancement due to the resonances. The asterisks are the Malinovsky et al. (1980) calculations (DW and semi-classical).

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thumbnail Fig. 9

Same as Fig. 4, for the strong forbidden 1–429 transition. The asterisk is the DW value calculated by Malinovsky et al. (1980).

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On the other hand, the strong forbidden transition from the ground state to the 3s 3p5 4s 2P3/2 does not have much resonance contribution, as we expected, i.e. the DW and R-matrix results are almost the same, as Fig. 9 shows. The DW calculation of Malinovsky et al. (1980) is about a factor of two lower.

thumbnail Fig. 10

Same as Fig. 4, for one of the important transitions to the 3s2 3p4 4p.

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As we expected, we find some resonance contribution for transitions to the 3s2 3p4 4p levels. Figure 10 shows an example of the excitation to a level producing one of the strongest lines (see Table 1).

thumbnail Fig. 11

Same as Fig. 4, for one of the important transitions to the 3s2 3p4 4d. The asterisk is the DW value calculated by Malinovsky et al. (1980).

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An enhancement is also present in the transitions to the 3s2 3p4 4d levels. Figure 11 shows one example, again for a level producing an observed line (see Table 1). Finally, Fig. 12 shows that little resonance contribution is present for the 3s2 3p4 4f levels.

thumbnail Fig. 12

Same as Fig. 4, for one of the important transitions to the 3s2 3p4 4f.

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We then built ion population models with the DW excitation rates and the R-matrix ones, together with the same set of radiative rates. The relative intensities are shown in the first and third intensity columns of Table 1. The effect of the resonances is obvious. The decay from the 3s2 3p4 4s 2D5/2 is enhanced by almost a factor of two.

4.4. Including the n = 5, 6 levels

thumbnail Fig. 13

The term energies of the target levels for the 62-configurations DW run (only 44 retained for the ion model).

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In order to include the main cascading contributions from the n = 5,6 levels in our ion model, we have run a full DW calculation (as explained in Sect. 2) with a set of 62 configurations included in the target CI expansion. We have determined collision strengths explicitly between the 1036 levels arising from the 44 configurations listed in Table 4 and displayed in Fig. 13. The excitation rates and radiative data to/from the n = 5,6 levels have been merged with the previous R-matrix run. The level populations were obtained, and the relative intensities for the selected lines are shown in Table 1 (RM+DW(n = 6) model). We confirm the results of Malinovsky et al. (1980), in that the inclusion of cascading from n = 5,6 levels increases the intensities of the decays from the 3s2 3p4 4s levels by about 20%, i.e. by a relatively small amount.

Table 4

The target electron configuration basis and orbital scaling parameters λnl for the 62-configurations DW run.

Malinovsky et al. (1980) provided some estimates of the contribution from even higher levels, and from recombination from Fe xi, however, they were even smaller.

4.5. The 3–429 3s 3p62S1/2–3s 3p5 4s 2P3/2 transition

As we have seen (cf. Fig. 9), the direct excitation from the ground to the 3s 3p5 4s 2P3/2 is large, when compared to those for the 3s2 3p4 4s levels. The 3s 3p5 4s 2P3/2 level decays with a strong dipole-allowed transition to the 3s 3p62S1/2 (3–429). The resulting intensity as calculated with our most extended model is still larger than the 3s2 3p52P3/2–3s2 3p4 4s 2D5/2 94.012 Å line. The same is true at higher densities. It is somewhat puzzling that the main decays of the 3s2 3p4 4s levels were first identified by Edlén (1937), but nobody has identified the stronger 3–429 line.

We have run various DW calculations for other ions along the Cl-like sequence and for other sequences, and found the same types of transitions to be very prominent but not identified. We have found possible identifications, which will be presented in a separate paper.

For Fe x, the 3–429 is the only line among all the decays from the 3s 3p5 4s levels to be easily detectable. The ab-initio wavelength of the n = 4 model is 91.5 Å. However, considering the relative differences between experimental and ab-initio energies of the 3s2 3p4 4s and 3s2 3p4 4p levels, we estimated that this line would fall around 95–96 Å.

We have searched extensively all experimental data, in particular those B.C. Fawcett plates where transitions from the 3s2 3p4 4s feature prominently. We found only one candidate, an unidentified iron line at 96.01, of about the same intensity as the nearby 96.12 Å iron line, identified by Edlén (1937). Behring et al. (1972) also observed two strong lines of the same intensity at 96.007 and 96.119 Å, while in all other solar measurements (e.g. Manson 1972; Malinovsky & Heroux 1973) these lines are blended.

The only other line within a few angstroms is the 95.37 Å line. This is a self-blend of two decays from the 3s2 3p4 4s levels, again identified by Edlén (1937). The combined intensity of these two lines at 1012 cm-3 is about the same as the 96.12 Å one, so the 95.37 Å cannot be further blended with the 3−429 transition.

We have carried out five increasingly large ab initio structure calculations just focussing on the 4s configurations. The idea was to calculate the energy difference between the 3s2 3p4 4s 4P5/2 and the 3s 3p5 4s 2P3/2 and then use the known energy of the former to estimate the wavelength of the transition from the latter state to 3s 3p62S1/2. The results of the five calculations, in order of increasing complexity, are 91.97, 95.58, 95.78, 95.86, 95.89 Å. These are the result of purely ab initio calculations without empirical adjustments, and provide strong support for the identification of the 3–429 line with the iron 96.007 Å line.

5. Summary and conclusions

We have presented the first complete calculations for n = 4,5,6 levels in Fe x. The calculation of accurate atomic data for the n = 4 levels has turned out to be quite complex and for the 3s2 3p4 4s, in particular, it required a large-scale R-matrix calculation. Given the small collision strengths for excitations from the ground, these levels are mainly affected in two ways. First, the rates are increased significantly by strong resonances which are attached mainly to the 3s2 3p4 4p levels. Second, the population of these levels is enhanced by cascading from higher levels, as already pointed out by Malinovsky et al. (1980).

It turns out that the previous calculation for the 3s2 3p4 4s levels, by Malinovsky et al. (1980), overestimated the collisional rates by about a factor of two. On the other hand, we found an increase of about a factor of two due to resonances. Resonances attached to higher levels not included in the present R-matrix calculations are not expected to make a large contribution. The intensity of the 94 Å as given with the n = 4 R-matrix data and cascading from n = 4,5,6 levels is only about 30% higher than currently calculated with CHIANTI.

We found that a large number of strong transitions are unidentified, as we saw in Fe ix (O’Dwyer et al. 2012). We have found strong evidence in support of the identification of the 3−429 3s 3p62S1/2−3s 3p5 4s 2P3/2 transition. We have found many new tentative identifications. These will be discussed in a separate paper.

The issues highlighted here are quite general in the sense that they apply to other ions along the Cl-like sequence and to other

iron ions. Resonance contributions are important for many low-lying n = 4 levels, in particular for the 3s2 3pq 4s levels. Decays from the 3s 3pq 4s levels are strong but have not been previously identified. Work is in progress to address these issues.

Acknowledgments

G.D.Z. acknowledges the support from STFC via the Advanced Fellowship programme. We acknowledge support from STFC for the UK APAP network. B. C. Fawcett is thanked for his contribution in rescuing some of his original plates, and for the continuous encouragement over the years.

References

All Tables

Table 1

List of a few among the strongest Fe x lines in the soft X-rays.

Table 2

The target electron configuration basis and orbital scaling parameters λnl for the R-matrix and DW runs for the n = 3,4 levels.

Table 3

Level energies for Fe x (n = 3,4).

Table 4

The target electron configuration basis and orbital scaling parameters λnl for the 62-configurations DW run.

All Figures

thumbnail Fig. 1

The main levels related to the 3s2 3p4 4s 2D5/2, which produces the 94.012 Å line. The values of the collision strengths at threshold among the levels and from the ground state are shown.

Open with DEXTER
In the text
thumbnail Fig. 2

The term energies of the target levels (32 configurations) for the n = 4 calculations. The 218 terms which produce levels having energies below the dashed line have been retained for the close-coupling expansion.

Open with DEXTER
In the text
thumbnail Fig. 3

Maximum relative difference (in percentage) between the thermally-averaged collision strengths from the ground state, calculated with an increasing number of energy points, from 2000 to 8000.

Open with DEXTER
In the text
thumbnail Fig. 4

Above: collision strength for the forbidden red coronal line, averaged over 0.1 Ryd in the resonance region. The data points are displayed in histogram mode. Boxes indicate the DW values. Below: thermally-averaged collision strengths, with other calculations.

Open with DEXTER
In the text
thumbnail Fig. 5

Same as Fig. 4, for the allowed 1−3 345.74 Å transition.

Open with DEXTER
In the text
thumbnail Fig. 6

Same as Fig. 4, for the strong forbidden 1–5 257.26 Å transition.

Open with DEXTER
In the text
thumbnail Fig. 7

Same as Fig. 4, for the allowed 1–30 174.53 Å transition, the strongest in the EUV.

Open with DEXTER
In the text
thumbnail Fig. 8

Same as Fig. 4, for the allowed 94.012 Å transition. Note the strong enhancement due to the resonances. The asterisks are the Malinovsky et al. (1980) calculations (DW and semi-classical).

Open with DEXTER
In the text
thumbnail Fig. 9

Same as Fig. 4, for the strong forbidden 1–429 transition. The asterisk is the DW value calculated by Malinovsky et al. (1980).

Open with DEXTER
In the text
thumbnail Fig. 10

Same as Fig. 4, for one of the important transitions to the 3s2 3p4 4p.

Open with DEXTER
In the text
thumbnail Fig. 11

Same as Fig. 4, for one of the important transitions to the 3s2 3p4 4d. The asterisk is the DW value calculated by Malinovsky et al. (1980).

Open with DEXTER
In the text
thumbnail Fig. 12

Same as Fig. 4, for one of the important transitions to the 3s2 3p4 4f.

Open with DEXTER
In the text
thumbnail Fig. 13

The term energies of the target levels for the 62-configurations DW run (only 44 retained for the ion model).

Open with DEXTER
In the text

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