Atomic data from the IRON project
LXVIII. Electron impact excitation of Fe XI^{}
G. Del Zanna^{1}  P. J. Storey^{2}  H. E. Mason^{1}
1  DAMTP, Centre for Mathematical Sciences, Wilberforce Road Cambridge, CB3 0WA, UK
2 
Department of Physics and Astronomy, University College London,
Gower Street, London, WC1E 6BT, UK
Received 28 July 2009 / Accepted 11 January 2010
Abstract
A new Rmatrix scattering calculation for electron
collisional excitation of Fe XI is presented and compared to
earlier calculations. The calculation includes 145 LS
terms and 465 finestructure levels and uses
the intermediatecoupling frame transformation method (ICFT).
We discuss the strong interactions that exist between three J=1levels in the 3s^{2} 3p^{3} 3d electron configuration. These levels
give rise to strong lines in the EUV spectrum and their energies and
identifications have been the source of much confusion in the
literature. We show that the oscillator and collision strengths
linking these levels to the ground levels of the ion are very
sensitive to the choice of configuration basis and argue that most
earlier calculations have failed to represent these levels adequately.
Key words: atomic data  line: identification  techniques: spectroscopic
1 Introduction
Fe XI is an important ion for the quiet solar corona because it produces strong spectral lines that can be used both for plasma diagnostics and for instrument calibration. Spectral lines from Fe XI have been recorded by many solar coronal missions (e.g. Skylab, SOHO), and are of particular importance for the recent Hinode mission, in particular the Extreme ultraviolet Imaging Spectrometer (EIS), as discussed e.g. in Young et al. (2007).
To date, there have been many scattering calculations for electron collisional excitation of Fe XI, all of which are unsatisfactory in some regard when comparisons are made with observations.
The first extensive work on this ion was from Mason (1975), who performed a distortedwave (DW) calculation using the University College London (UCL) suite of codes. This work enabled Mason & Nussbaumer (1977) to confirm line identifications in the EUV.
Bhatia & Doschek (1996, hereafter BD96) performed a DW calculation using the same codes, and a basic set of 4 electron configurations (3s^{2} 3p^{4}, 3s 3p^{5}, 3s^{2} 3p^{3} 3d, 3p^{6}) for their scattering calculation. These calculations were then extended by Bhatia et al. (2002, hereafter BDE02) by including some n=4 levels, for a total of 96 finestructure levels.
Gupta & Tayal (1999a,b) calculated collision strengths for transitions between 38 finestructure levels using a semirelativistic Rmatrix approach. Large differences with the DW results of Bhatia & Doschek (1996) were found, partly due to the resonance contribution, partly due to the use of a different target and configuration basis. GT99 adopted a 20 LS state target, expanded in a 78state basis, from Deb & Tayal (1998, hereafter DT98). We note that this 20 state calculation is not actually described in Deb & Tayal (1998) but as discussed below, is not in good agreement with the experimental data. Moreover, the GT99 calculation was incomplete from an application point of view, because it did not include the important ^{5}D, ^{3}G and ^{1}G LS terms. Some of the levels originating from these terms are metastable and it is necessary to include them when calculating the level populations. Aggarwal & Keenan (2003a,b) used an 8configuration basis for their scattering calculation, in which they included configurationinteraction (CI) among the four main spectroscopic configurations and the additional 3s^{2} 3p^{2} 3d^{2}, 3s^{2} 3p^{3} 4s, 3s^{2} 3p^{3} 4p, and 3s^{2} 3p^{3} 4d configurations. There are various problems with the above calculations, mostly due to the strong interactions present between some Fe XI levels, as described below.
2 The target and the line identifications
The construction of a good target has been particularly challenging for this ion. This is because the energies of a large number of finestructure levels have remained unknown experimentally, and there is strong level mixing among some levels, in particular for the three energetically highest J=1 levels in the 3s^{2} 3p^{3} 3d configuration. These levels are important because they give rise to some of the strongest Fe XI spectral lines, which fall in the EUV.
As part of the preliminary work to identify the best target we reassessed all the literature and experimental data not only for Fe XI, but also for many of the ions along the same S Ilike isoelectronic sequence. Most previous line identifications have been made using laboratory measurements. For the Fe ions in particular see the work by Fawcett and the group at the Culham laboratories in the 1960's and 70's (see, e.g. Fawcett & Gabriel 1965; Gabriel et al. 1965; Fawcett & Gabriel 1966; Gabriel et al. 1966; Bromage et al. 1977). Further work has been produced by a few other authors (e.g. Jupén et al. 1993; Träbert et al. 2003), however some level and line identifications were contradictory.
The spectra obtained at the Culham laboratories were not free from impurities, but had an excellent spectral resolution and are still the best available to identify lines that are formed in highdensity plasmas. As part of the assessment we have reanalysed some of the original plates, and used some unpublished material from Fawcett. The spectral resolution was slightly better than the quietSun integrated rocket spectrum of Behring et al. (1976) which has become the basic reference for many wavelength measurements. The result of this work, and in particular what we refer to here as our experimental energies , will be published in a separate paper (Del Zanna 2010).
2.1 Previous structure calculations
The main (spectroscopically important) configurations for Fe XI are 3s^{2}3p^{4}, 3s 3p^{5}, 3s^{2}3p^{3}3d, and 3p^{6}, which give rise to 48 finestructure levels. Decays from 3s 3p^{5} and 3s^{2}3p^{3}3d to the ground configuration 3s^{2}3p^{4} produce strong EUV lines. Additional lines in the Xray are produced mostly by decays from n=4 levels.
Bromage et al. (1977) used Cowan's HartreeFock (HF) atomic structure code with the Slater parameters optimization procedure to provide experimentallyadjusted energies for the 3s^{2} 3p^{3} 3d levels, and oscillator strengths for transitions from these levels to the ground configuration. This was an excellent piece of work, showing the importance of combining laboratory measurements with atomic structure calculations, something rarely found in the literature. Fawcett (1986) used the HartreeFockRelativistic code of Cowan with the Slater parameters optimization procedure to provide 3s^{2} 3p^{3} 3d level energies and oscillator strengths for 3s^{2} 3p^{4}3s^{2} 3p^{3} 3d transitions in various ions of the S Ilike sequence. The adjustments took into account the experimental wavelengths available at that time, and only included CI among the main four configurations and the additional 3s 3p^{4} 3d, 3p^{5} 3d, 3s 3p^{3} 3d^{2} and 3s^{2} 3p^{3} 4s configurations.
Mendoza & Zeippen (1983) calculated transition probabilities for the forbidden transitions in the ground configuration along the isoelectronic sequence by using SUPERSTRUCTURE (see Eissner et al. 1974; Nussbaumer & Storey 1978) and a set of eight configurations.
BD96 used a basic set of four configurations within SUPERSTRUCTURE. These calculations were then extended by BDE02 by including some n=4 levels, for a total of 96 finestructure levels. We note that this extension did not significantly alter oscillator strengths for transitions to the 3s^{2} 3p^{3} 3d levels, i.e. did not improve the representation of the n=3 configurations.
Fritzsche et al. (2000) calculated transition probabilities for forbidden and allowed Fe XI transitions using the GRASP92 atomic structure code and a multiconfiguration DiracFock (MCDF) approach. Unfortunately, no adjustments to experimental energies were applied, nor experimental wavelengths used in the calculations of the transition probabilities. Large discrepancies (more than 50 Å) between their calculated wavelengths and the observed ones are present, particularly for the forbidden lines.
Table 1: Electron configuration basis for the benchmark calculation (48C) and orbital scaling parameters.
DT98 calculated ab initio energies and oscillator strengths with the CIV3 atomic structure code by initially including all configurations (up to n=4) with 2electron excitations from the basic four configurations.
2.2 Our target
We have carried out a large number of structure calculations with different sets of configurations and orbitals using SUPERSTRUCTURE and AUTOSTRUCTURE (Badnell 1997). We found that the positioning and mixing of some levels changes considerably, strongly affecting energies and oscillator strengths. We have also made structure calculations using the same set of configurations as those reported in literature, and obtained similar energies and oscillator strengths, thus confirming that the large differences between different calculations were mainly due to the different sets of configurations included and not to the use of different approximations and codes.
As our best ``benchmark'' configuration basis we have chosen the 48 configurations (48C) listed in Table 1 and used AUTOSTRUCTURE. The scaling parameters, , for the potentials in which the orbital functions are calculated are given in Table 2. A positive scaling parameter indicates a statistical model potential while a negative scaling parameter signifies a correlation orbital that is calculated in a Coulomb potential with central charge number where Z = 26. The scaling parameters were chosen to minimise the equally weighted sum of the energies of the 24 lowest LS terms. Table 3 clearly shows good agreement between the energies and our experimental energies (Del Zanna 2010), in particular in terms of relative differences between levels.
In order to further improve the energies (and help the identification process), we have also applied term energy corrections (TEC) based on the observed energies of Del Zanna (2010) (48CT). The TEC procedure (see, e.g. Zeippen et al. 1977; Nussbaumer & Storey 1978) introduces empirical corrections to the LS Hamiltonian matrix. The energies (TEC) are also shown in Table 3.
We then searched for a more limited set of configurations which provided energies (and weighted oscillator strengths gf) as close as possible to our 48CT calculation. We identified the basis of 13 configurations (13C) listed in Table 2. This was used as the target basis for our scattering calculation. The energies from our target calculation (13C) agree well with those from the benchmark calculation and our experimental energies (Del Zanna 2010), as shown in Table 3. Recently, Ishikawa & Vilkas (2008) have published theoretical level energies for ions along the S Ilike sequence obtained with the relativistic multireference manybody perturbation theory (hereafter referred to as MRMP). This procedure yields very accurate energies, as known from previous work (see Ishikawa & Vilkas 2001; Del Zanna & Mason 2005, for Fe XII; Del Zanna & Ishikawa 2009, for Fe XVII; Ishikawa et al. 2009, for ions along the Ne Ilike sequence). Table 3 clearly shows good agreement between our experimental energies (Del Zanna 2010) and those calculated by the MRMP method. This confirms the reliability of our experimental energies (which were obtained independently before the MRMP ones were published).
Table 2: The target electron configuration basis (13C) and orbital scaling parameters.
Table 4 lists the weighted oscillator strengths (gf) for a few of the most important transitions from the five levels of the ground configuration obtained from our benchmark basis (with and without TEC) and from the target basis. A remarkably good agreement between the gf values obtained with our target and benchmark calculations can be seen. Table 4 also lists gf values calculated by DT98, AK03, BDE02. Large differences are found for all the transitions from highly mixed levels. This includes for example the strong ^{3}P_{2}^{3}P (138) transition for which AK03 calculated a gf of 3.4 and BDE02 of 4.0 compared to our best value of 2.5. The special case of the three highly mixed J=1 levels is discussed in detail in the following Section. Note that the gf values obtained by F86 are often more accurate than any of the previous abinitio calculations, because experimental adjustments were applied.
Table 3: List of energies (cm^{1}) for the lowest 48 levels of Fe XI.
The large differences in gf values are directly reflected in large differences in collision strengths as we shall discuss later. This occurs because the main contribution for strong dipoleallowed transitions comes from high partial waves, where the collision strength is approximately proportional to the gf value for the transition.
Given that gf values from our target calculation are very similar to those of the benchmark + TEC one, it follows that transition probabilities are also very similar. Mixing and level ordering changes with any experimental adjustement, so transition probabilities to be associated with the present scattering calculation were calculated from the target calculation, by only adding all spinspin interactions within the lowest four configurations, and by replacing energies with the experimental ones of Del Zanna (2010), whenever available.
Table 4: Weighted absorption oscillator strengths (gf).
2.3 Identification of the three 3s^{2} 3p^{3} 3d J = 1 levels
The strength of the interaction between levels of the same J and parity depends, to a first approximation, on the inverse of the energy difference between them. There are three J=1 levels (indices 37, 39, 41 in Table 3) within the 3s^{2} 3p^{3} 3d which lie very close in energy, and hence interact strongly. This makes the definition of a good target, which represents these levels well, challenging. Another complexity lies in the fact that levels change their percentage composition and energy ordering along the isoelectronic sequence, as shown in Fig. 2. These results were obtained with AUTOSTRUCTURE applying the same benchmark basis (with correlation orbitals) and minimization procedure to all the ions in the sequence.
Whilst the lower and upper J=1levels are so strongly interacting that no designation in LS terms is meaningful, the middle J=1 3s^{2} 3p^{3} (^{2}D) 3d ^{3}S level remains identifiable throughout the sequence and becomes the ``middle'' J=1 level for Fe XI.
The ``labelling'' used for these levels varies in the literature, however we prefer to call them ``lower, middle and upper J=1 level'' here, the ordering being their energy relative to the ground state (our levels 37, 39 and 41 respectively).
To establish the identifications and energies of the mixed J=1levels we started by confirming the identification of the 3s^{2} 3p^{3} (^{2}D) 3d ^{3}P level (38 in Table 3). This level produces two strong decays to the ground ^{3}P levels (138 and 238). The 138 line is observed at 188.216 Å and is the second strongest Fe XI line in lowdensity plasmas. The 238 transition is observed at 192.813 Å, in exact agreement with the splitting between the ground ^{3}P levels, known from the strong forbidden line at 7891.8 Å.
The separation between the ^{3}P levels calculated in the 48C basis suggests an energy for the upper J=1 level in broad agreement with the value 541 410 cm^{3} derived by Bromage et al. (1977) and based on the following correct assignments made by those authors: 241: 189.129 Å; 341: 189.735 Å; 441: 198.549 Å. Jupén et al. (1993) labelled this level ^{1}P and incorrectly identified the 241 and 441 transitions with the lines observed at 192.619 and 202.405 Å in the laboratory spectra. BD96 had the same correct assignment as Bromage et al. (1977).
Figure 2: Difference between the theoretical energies of the three 3s^{2} 3p^{3} 3d J=1 levels and the theoretical energy of the 3s^{2} 3p^{3} (^{2}D) 3d ^{3}P (level 38 in Table 3) along the S Ilike sequence. The energies were calculated with SUPERSTRUCTURE and the same 48 configuration basis (our benchmark calculation, 48C). 
The middle J=1 level 3s^{2} 3p^{3} (^{2}D) 3d ^{3}S (39) produces four observable transitions: 439, 139, 239, 339, correctly identified by Bromage et al. (1977) with the lines observed at 201.737, 187.446, 192.020 and 192.641 Å. Jupén et al. (1993) instead incorrectly identified the 139 transition with the line observed in the laboratory spectra at 184.704 Å. Note that the labelling for this level given by Jupén et al. (1993) was ^{3}P . BD96 had the same correct assignment as Bromage et al. (1977). Keenan et al. (2005) incorrectly identified the 239, 339 transitions with the lines observed at 189.19 and 189.72 Å respectively.
The lowest J=1 level (level 37) is the most complex one, since the oscillator strength for its decay to the ground state is very sensitive to mixing. The gf values obtained in the benchmark, 48CT, calculation suggest that this transition should be third strongest from this ion. We identify this transition (137) with the strong 188.299 Å line. This line is very close to the 138 transition (188.216 Å), and is about 70% its intensity. The ratio in gf values means that (neglecting cascading) we predict a relative intensity of 60%, not too far from the measured value. Notice that AK03 and DT98 predict about 20% and 50% respectively.
Bromage et al. (1977) had a calculated wavelength for the 137 transition of 188.40 Å, very close to the actual value (188.299 Å), however they identified it with a weaker line observed at 189.940 Å. This error was caused by the fact that the 188.299 Å line was incorrectly assigned to an Fe XII transition. BD96 also gave the same incorrect assignment. Jupén et al. (1993) correctly identified this level, although they gave it an incorrect labelling (^{3}S ) which has caused confusion in the literature.
As we have already seen, Ishikawa & Vilkas (2008) provided very good level energies, however in terms of identifications there are a few incorrect assignments, which originated from previous literature (Ishikawa, priv. comm.). Furthermore, the comparisons listed in Ishikawa & Vilkas (2008) between their results and those of Jupén et al. (1993) were not appropriate because the assignments followed the labelling of the levels given by Jupén et al. (1993), rather than their order in energy.
In terms of labelling, the National Institute of Standards and Technology (NIST) version 3 database^{} provides incorrect assignments for the three J=1 levels. However, in terms of wavelength assignments, it provides correct identification for the middle and upper J=1 levels, because the original assignments of Bromage et al. (1977) were adopted.
3 The scattering calculation
The Rmatrix 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 shifts. The configuration basis describing the target for the present calculation is shown in Table 2 and Fig. 1. We used the AUTOSTRUCTURE code (Badnell 1997) to obtain the target radial wavefunctions using radial scaling parameters to minimize the equallyweighted sum of all LS term energies as listed in Table 2. The energies of the target terms are listed in Table 5, together with the experimental ones (Del Zanna 2010), which were used within the calculation to accurately position the resonance thresholds.
The set of 13 electron configurations gives rise to 465 LS terms and 1103 finestructure levels. For the scattering calculation we have retained only the lowest 145 LS terms, which give rise to 365 levels and 66 430 transitions. The expansion of each scattered electron partial wave was done over a basis of 25 functions within the Rmatrix boundary, and the partial wave expansion extended to a maximum total orbital angular momentum quantum number of L=16.
The outer region calculation used the intermediatecoupling frame transformation method (ICFT) described by Griffin et al. (1998), in which the transformation to intermediate coupling uses the socalled termcoupling coefficients (TCCs), and is complete up to a total angular momentum quantum number, J=23/2. We have supplemented this calculation, which includes exchange, with a nonexchange calculation that extends from J=25/2 to J=73/2. Dipoleallowed transitions were toppedup to infinite partial wave using an intermediate coupling version of the CoulombBethe method as described by Burgess (1974) while nondipole allowed transitions were toppedup assuming that the collision strengths form a geometric progression in J for J>73/2(see Badnell & Griffin 2001).
Table 5: Theoretical energies of target terms (Rydberg), with the experimental energies adopted for the scattering calculation. Only the terms from the lowest 4 configurations are shown here.
Figure 4: Collision strengths for transitions within the ground configuration, averaged over 1 Ryd. Boxes indicate the GT99 values, while triangles the AK03 ones. 
Figure 5: Collision strengths for a selection of 3s^{2} 3p^{4}3s 3p^{5} transitions, averaged over 1 Ryd. Boxes indicate the GT99 values, while triangles the AK03 ones. 
3.1 Collision strengths
The Rmatrix calculation extended to an incident electron energy of 141 Ry. At higher energies we used the method of scaling and extrapolating to the appropriate highenergy limits as described in Burgess & Tully (1992). The highenergy limits were calculated with AUTOSTRUCTURE for both opticallyallowed (see Burgess et al. 1997) and forbidden transitions (see Chidichimo et al. 2003).
The collision strengths of all the transition from the levels of the ground configuration have been visually inspected, to check that the values converged to the respective highenergy limits.
Figure 3 shows as an example the collisions strengths of the 12 transition in the resonance region. Notice the large number of resonances. Figures 47 show a sample of collision strengths, averaged over 1 Ry for an easier comparison with literature data. At energies above all resonances, good agreement was found with the values calculated by GT99 and AK03 for transitions within the ground configuration (see Fig. 4), with the exception of the ^{3}P_{0}^{1}S_{0} values calculated by GT99. Good agreement is found for the transitions to 3s 3p^{5} calculated by GT99 (see Fig. 5), with some differences with the AK03 values. Larger differences are found for transitions to the 3s^{2} 3p^{3} 3d levels (see Fig. 6). The large discrepancies seen in the gf values for the especially ``troublesome'' transitions to the J=1 levels are reflected in the large discrepancies in the collision strengths seen in Fig. 7.
Figure 6: Collision strengths for a selection of 3s^{2} 3p^{4}3s^{2} 3p^{3} 3d transitions, averaged over 1 Ryd. Boxes indicate the GT99 values, while triangles the AK03 ones. 
Figure 7: Collision strengths for transitions involving the three J=1 levels, averaged over 1 Ryd. Boxes indicate the GT99 values, while triangles the AK03 ones. 
Table 6: Effective collision strengths for a selection of transitions from the ground state, at 4 temperatures (log T[K] = 5.7, 6.0, 6.3, 6.7; ).
3.2 The effective collision strengths
We calculated the temperaturedependent effective
collision strength
by assuming a
Maxwellian electron distribution:
where E_{j} is the final energy of the colliding electron (after excitation has occurred) and k is the Boltzmann constant. We performed the numerical integration by linearly interpolating the data points and extrapolating to the highenergy limit.
The effective collision strengths were calculated in a wide temperature range ( K) to cover all astrophysical applications. A selection of values for transitions from the ground state up to the 3p^{6} ^{1}S_{0} level (48) are shown in Table 6 (the full dataset is available online). Given that results obtained with the intermediatecoupling frame transformation are known to be comparable in accuracy to those obtained using a full BreitPauli Rmatrix calculation, the main uncertainty in the rates derives from the accuracy of the target. Rates for most strong transitions are expected to have a relative accuracy of 10% or so, although those involved with the highly mixed levels 37, 39, 41 are expected to be less accurate. Comparison with experimental data (Del Zanna 2010) indicates agreement within 20% for most line intensities, which is encouraging.
Figures 811 show effective collision strengths for the same selection of transitions for which we plotted collision strengths. In Fig. 12 we plot our effective collision strengths for dipoleallowed transitions at 10^{6} K against the AK03 values. Strong transitions with differences of more than a factor of two are labelled. In Fig. 13 we plot our effective collision strengths for dipoleallowed transitions at two temperatures against the GT99 values. In Fig. 14 we plot our values for forbidden transitions at a low temperature, against the AK03 and GT99 values.
Figure 8: Effective collision strengths for transitions within the ground configuration. Boxes indicate the GT99 values, while triangles the AK03 ones. 
Figure 9: Effective collision strengths for a selection of 3s^{2} 3p^{4}3s 3p^{5} transitions. Boxes indicate the GT99 values, while triangles the AK03 ones. 
Figure 10: Effective collision strengths for a selection of 3s^{2} 3p^{4}3s^{2} 3p^{3} 3d transitions. Boxes indicate the GT99 values, while triangles the AK03 ones. 
Figure 11: Effective collision strengths for transitions involving the three J=1 levels. Boxes indicate the GT99 values, while triangles the AK03 ones. 
Significant differences with the Rmatrix calculations of GT99 and AK03 are found for a large number of transitions. The largest (more than a factor of two) differences are, as expected from the large discrepancies seen in the gf values, for the ``troublesome'' transitions to the J=1 levels (Figs. 1113). We believe that most of the differences at 10^{6} K are due to the different target basis.
At high temperatures, the AK03 values tend to have the correct behaviour overall, while the GT99 values for all the strong dipoleallowed transitions are underestimated as shown in Figs. 911, 13. This does not occur for the forbidden transitions (see Figs. 8, 14). The fact that good agreement in the collision strengths is found at low energies possibly means missing high partial wave and/or high energy contributions to the dipoleallowed collision strengths in the work of Gupta & Tayal (1999b). The same finding is reported in a study of Fe XIII by Storey & Zeippen (2009).
Figure 14: Comparison of effective collision strength for forbidden transitions at K. Transitions with values differing by more than a factor of 2 are labelled with our level indices. 
At low temperatures, and in particular for the forbidden transitions, very large differences are found, in particular with the AK03 values which are consistently lower, as Fig. 14 shows. The most likely explanation is the additional resonances present in our calculation due to the larger number of target states, which are particularly significant at lower temperatures.
3.3 Convergence on energy resolution
Several calculations of the collision strengths were made using different energy resolutions. A coarse mesh of 0.75 Ry was used beyond the resonance region of the exchange calculation and over the entire energy range of the nonexchange calculation up to an energy of 141 Ry in all the calculations. In order to test the importance of the energy resolution in the resonance region, the number of energy points was increased from 2000 up to 32 000 in steps of 2000 points. For each of these cases, we calculated the final collision strength and the thermallyaveraged ones. We have then considered all the transitions from the ground configuration to the other spectroscopicallyimportant configurations shown in Table 3, and calculated the maximum deviation of the thermallyaveraged collision strength for a set of temperatures. The results are shown in Fig. 15, where it is clear that for a number of mesh points larger than 16 000 the maximum deviation is less than 10% at all temperatures.
4 Summary and conclusions
A number of scattering calculations for electron collisional excitation of Fe XI have been produced in the literature, none of which have been able to correctly represent the excitation for some of the most important levels for the EUV spectrum of this ion.
After a long iterative procedure in which we combined experimental data with structure calculations along the S Ilike sequence, we have been able to identify a good basis for our scattering calculations, and to provide reliable energies and oscillator strengths.
During this procedure we were able to identify most of the previously unknown finestructure levels within the important 3s^{2}3p^{3}3d configuration, which gives rise to strong EUV transitions observed for example by Hinode/EIS.
In terms of collision strengths, we find large differences with values found in previous literature, in particular for those few transitions arising from levels highly mixed and very sensitive to the target. We believe that several outstanding discrepancies between astronomical observations and theory are resolved with this new calculation, as described in Del Zanna (2010).
G.D.Z. acknowledges support from STFC via the Advanced Fellowship program. We acknowledge support from STFC (UK) via the APAP network grant. We thank N. R. Badnell for various advices on the calculations. G.D.Z. warmly thanks B. C. Fawcett for continuous support and encouragement, together with many exchanges of correspondence.
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Footnotes
 ... XI^{}
 Detailed tables of the present data are available in electronic form at the CDS via anonymous ftp to cdsarc.ustrasbg.fr (130.79.128.5) or via http://cdsweb.ustrasbg.fr/cgibin/qcat?J/A+A/514/A40
 ... database^{}
 http://physics.nist.gov
All Tables
Table 1: Electron configuration basis for the benchmark calculation (48C) and orbital scaling parameters.
Table 2: The target electron configuration basis (13C) and orbital scaling parameters.
Table 3: List of energies (cm^{1}) for the lowest 48 levels of Fe XI.
Table 4: Weighted absorption oscillator strengths (gf).
Table 5: Theoretical energies of target terms (Rydberg), with the experimental energies adopted for the scattering calculation. Only the terms from the lowest 4 configurations are shown here.
Table 6: Effective collision strengths for a selection of transitions from the ground state, at 4 temperatures (log T[K] = 5.7, 6.0, 6.3, 6.7; ).
All Figures
Figure 1: The energetically lowest electron configurations of Fe XI. The energies are those of the benchmark calculation (48C), with all orbitals treated as spectroscopic. Configurations included within the target basis are highlighted in bold. Notice that the last two of the 13 target configurations are not shown in the plot, because they lie at higher energies, mixed with many other configurations. The 3s^{2} 3p^{2} 3d 4p levels start at 15.14 Ryd, while those of the 3s^{2} 3p^{2} 3d 4f configuration at 17.57 Ryd. The 145 terms which produce levels having energies below the dashed line have been retained for the scattering calculation. 

In the text 
Figure 2: Difference between the theoretical energies of the three 3s^{2} 3p^{3} 3d J=1 levels and the theoretical energy of the 3s^{2} 3p^{3} (^{2}D) 3d ^{3}P (level 38 in Table 3) along the S Ilike sequence. The energies were calculated with SUPERSTRUCTURE and the same 48 configuration basis (our benchmark calculation, 48C). 

In the text 
Figure 3: Collision strength for the 12 transition. 

In the text 
Figure 4: Collision strengths for transitions within the ground configuration, averaged over 1 Ryd. Boxes indicate the GT99 values, while triangles the AK03 ones. 

In the text 
Figure 5: Collision strengths for a selection of 3s^{2} 3p^{4}3s 3p^{5} transitions, averaged over 1 Ryd. Boxes indicate the GT99 values, while triangles the AK03 ones. 

In the text 
Figure 6: Collision strengths for a selection of 3s^{2} 3p^{4}3s^{2} 3p^{3} 3d transitions, averaged over 1 Ryd. Boxes indicate the GT99 values, while triangles the AK03 ones. 

In the text 
Figure 7: Collision strengths for transitions involving the three J=1 levels, averaged over 1 Ryd. Boxes indicate the GT99 values, while triangles the AK03 ones. 

In the text 
Figure 8: Effective collision strengths for transitions within the ground configuration. Boxes indicate the GT99 values, while triangles the AK03 ones. 

In the text 
Figure 9: Effective collision strengths for a selection of 3s^{2} 3p^{4}3s 3p^{5} transitions. Boxes indicate the GT99 values, while triangles the AK03 ones. 

In the text 
Figure 10: Effective collision strengths for a selection of 3s^{2} 3p^{4}3s^{2} 3p^{3} 3d transitions. Boxes indicate the GT99 values, while triangles the AK03 ones. 

In the text 
Figure 11: Effective collision strengths for transitions involving the three J=1 levels. Boxes indicate the GT99 values, while triangles the AK03 ones. 

In the text 
Figure 12: Comparison of effective collision strengths for dipoleallowed transitions at T=10^{6} K, compared to AK03. Strong transitions with values differing by more than a factor of 2 are labelled with our level indices. 

In the text 
Figure 13: Comparison of effective collision strength for dipoleallowed transitions at two temperatures, compared to GT99. Strong transitions with values differing by more than a factor of 2 are labelled with our level indices. 

In the text 
Figure 14: Comparison of effective collision strength for forbidden transitions at K. Transitions with values differing by more than a factor of 2 are labelled with our level indices. 

In the text 
Figure 15: Maximum relative difference between the thermallyaveraged collision strengths calculated with 36 000 mesh points in the resonance region, and a number of increasing mesh points from 2000 to 24 000. Only transitions from the 3s^{2}3p^{4} levels to 3s^{2}3p^{4}, 3s 3p^{5}, 3s^{2}3p^{3}3d and 3p^{6} were considered. 

In the text 
Copyright ESO 2010