The overall aims and methods of the project were summarized in the first paper of the IP series (Hummer et al. [1993]). The current paper is the first in a short IP sub-series presenting collisional data for C, N and O-like iron using essentially similar techniques and approximations.
In this connection, C-like iron Fe XXI is of particular interest from both
the theoretical and observational point of view. On the observational side,
lines of Fe XXI have been seen in both solar flares (e.g. Mason et al. [1979]; Cheng & Pallavicini [1988]; Cheng
et al. [1979])
and the coronae of cool stars, particularly that of Capella (Linsky et al. [1998]). In their analysis, Linsky et al. report on discrepant
results obtained
from the 
1354 line as compared with the Fe XXI EUV lines.
They suggest four possible explanations for the discrepancy, one of which,
inaccurate or incomplete atomic data, they rule out on the grounds that the
available data (Aggarwal [1991]; Aggarwal et al. [1997]) are good to 10%. As we
shall see, this error estimate is too optimistic due to the omission of high
energy resonant contributions to the collisional data.
In addition, the oscillator strengths provided by Aggarwal et al. ([1997])
differ markedly (up to six orders of magnitude) from the earlier work of
Bhatia et al. ([1987]). Aggarwal et al. in fact indicate that
their results
are accurate to 20% for the stronger transitions and state that it
would be desirable to have collisional data of comparable accuracy for the
higher lying levels. Our oscillator strengths are in good agreement with
those of Aggarwal et al. and we hope to go some way to fulfilling the latter
need in the current paper. Very recently Aggarwal & Keenan
([1999]) have published
new results for this iron ion on the basis of an extended Dirac R-matrix
calculation but only for the region where all channels are open. Their
collision strengths are in good agreement with the earlier work for the
strong transitions but there are discrepancies for the weaker transitions.
Since they do not, as yet, include resonance effects a detailed comparison
is not made here.
On the other hand, Zhang & Sampson ([1996], [1997]) provide extensive tables of collision and oscillator strengths for C-like ions including Fe XXI. They present results for all n=2-3 transitions calculated in a relativistic distorted wave approximation. Since these represent a complete set of data they complement the present calculations and those of Aggarwal ([1991]). We compare with these data at high energy to provide some further indication as to the accuracy of the available collisional data.
The first distorted wave calculation was performed by Mason et al. ([1979]). Their calculation was extended to higher levels by Bhatia et al. ([1987]) although, as noted earlier, their oscillator strengths are discrepant in many cases. They tabulate the collision strength at a single energy. The distorted wave approximation is well suited to this highly ionized system although it does omit resonance effects thus underestimating collision rates. With this proviso the Mason et al. data for the background cross sections are in fact reasonably accurate as has been shown by Aggarwal ([1991]). On the other hand, the distorted wave collision rates can be in error by up to an order of magnitude because of this omission of resonances. The original Mason et al. ([1979]) work does suffer from lack of convergence in J for some forbidden transitions at high energies/temperatures. Also the use of an algebraic transformation from LS to intermediate coupling means that the data for the transitions which are not allowed in LS coupling but which are permitted in intermediate coupling are inaccurate. The former point has been corrected by a further distorted wave calculation undertaken by Phillips et al. ([1996]) who extended the calculation further to include some n=4 levels. They seem to have been unaware of the earlier work of Aggarwal ([1991]) who obtained accurate collision strengths for the n=2levels in a fully-relativistic Dirac formulation using the R-matrix code of Wijesundera et al. ([1991]). This calculation includes resonance effects and the paper includes a detailed discussion and comparison with the work of Mason et al. ([1979]).
A comparison of our own and Aggarwal's ([1991]) data will thus allow us to investigate the two different approaches to the relativistic problem, the Dirac and Breit-Pauli approximations. Aggarwal ([1991]) has made a detailed comparison with the distorted wave results of Mason et al. ([1979]) and has already emphasized the importance of the resonance contributions and the correct treatment of intermediate coupling. The current work also demonstrates the necessity of including resonant contributions from higher-lying configurations, a point made by Aggarwal et al. ([1997]).
In the next section, we give a short description of the present calculation which is followed by a discussion of the results. Here we concentrate on a comparison with the work of Aggarwal ([1991]) since he has provided an excellent commentary on the earlier distorted wave results and with the newer, comprehensive relativistic distorted wave data of Zhang & Sampson ([1996], [1997]).
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