Numerous papers for the transition dealt with here
have appeared over the past 10 years or so. These have all been based on
essentially the same R-matrix suite of programs as the one we use, but with
different target wavefunctions.
Obviously it is important to compare some of this earlier work with ours,
especially in those cases where there exist significant differences between
the 
results.
Note that the comparisons we make concern calculations in which the target
wavefunctions have more than two terms.
The three ions we have selected for comparison, namely those corresponding to Z = 14, 26 and 28, have been studied by Mohan and collaborators: Si+5 (Mohan & Le Dourneuf 1990), Fe+17 (Mohan et al. 1987), Ni+19 (Mohan et al. 1990). Each of these raises questions which we now comment on.
Mohan & Le Dourneuf (1990) tabulate the effective collision
strength
for Si VI as a function of temperature. They calculated
using the collision strength they had obtained earlier by means of a 16 state
close-coupling expansion in LS coupling.
As can be seen in Fig. 11, where we plot as a function of
log
, their tabulated results rise dramatically with temperature when
this exceeds about 
. Burgess et al. (1991) were able to
make a reliable spline fit to Mohan & Le Dourneuf's data using the
program OMEUPS (see Burgess & Tully 1992), the r.m.s. error of the fit being
2.2%. In order to get a fit to this accuracy
Burgess et al. (1991) omitted
the lowest two temperature points given in the table. Mohan (private
communication) had previously informed one of us (JAT) that the published
value at the lowest temperature, i.e. 
, was
unreliable. However he gave no explanation why this was so.
Saraph & Tully (1994) state that at higher temperatures (not energies, as
printed incorrectly in their paper) the results of
Mohan & Le Dourneuf (1990)
indicate a steep rise in the effective collision strength that is due to
resonances converging on higher target states (i.e. on terms above
). The present investigation shows, however, that the reason
for the increase manifested by the starred data points in Fig. 11 is
principally due to the fact that
Mohan & Le Dourneuf (1990) used the
trapezoidal rule to carry out the integration over energy. Since there is a
big gap in their tabulation of 
between about 10 Ry and 48 Ry,
this numerical method should not have been used;
see
Burgess et al (1997b) for a detailed explanation.
The gap is apparent in Fig. 12a where we plot
as a function of energy: the collision strength
is taken from the atomic databank at The Queen's University of Belfast (QUB).
The gap is spanned in the figure by a dashed straight line. The resonances
above 48 Ry in Fig. 12a, i.e. 
the highest target term included
by Mohan & Le Dourneuf, are clearly responsible for the peak in
near 
seen in Fig. 11 (curves a and b).
The origin and
physical significance, if any, of these resonances have not been explained by
Mohan and Le Dourneuf. Fig. 12b shows that, as is to be expected,
from the IRON Project has no structure in the region beyond about
12 Ry. Consequently the resulting curve c in Fig. 11 does not have a peak
in the region of .
Figure 11: 
: Using
Mohan & Le Dourneuf's (1990)
from the QUB atomic databank and a) the trapezoidal rule,
b) the linear interpolation
method. 
: Mohan & Le Dourneuf (1990);
c) IRON Project
Figure 12: : a) by
Mohan & Le Dourneuf (1990) from
the QUB atomic databank; b) IRON Project
Saraph & Tully (1994) state that the effective collision
strength given by Mohan et al. (1987) rises steeply at higher energies. This
is wrong on two counts. Firstly, since the effective collision strength
is a function of T they should have said "at higher temperatures'' and not
"at higher energies''. Secondly, the effective collision strength that
Mohan et al. (1987) tabulate does not vary enormously with temperature.
As can be seen in Fig. 13, where we show versus log from
Mohan et al. (1987) and the IRON Project, rises only slightly at
temperatures above one million degrees. The effective collision strength from
Mohan et al. (1987) lies about 10% lower than the present one. This may be
due to the fact that they include less target terms in their close-coupling
expansion and use a much coarser energy mesh than we do.
Figure 13: 
: a) Mohan et al. (1987);
b) IRON Project
In Figs. 14 and 15 we compare the collision strength by Mohan et al. (1987) from the QUB atomic databank with the present calculation.
Figure 14: : a) by
Mohan et al. (1987) from the QUB
atomic databank; b) IRON Project
Figure 15: : a)
by Mohan et al. (1987) from the QUB
atomic databank; b) IRON Project
Mohan et al. (1990) tabulate for this ion
as a function of T. The range covered is from T = 104 to T = 107.
Now according to Arnaud & Rothenflug (1985) Ni XX has its maximum
coronal abundance at about 
, so the tabulation by
Mohan et al. does not cover the temperature range of interest fully.
Figure 16 shows as a function of log.
The starred points () correspond to data taken from Table 1 in
Mohan et al. (1990), while the full line curve represents the present results.
Both sets of results have a maximum at a temperature below log
.
Although the maxima occur at approximately the same value of log,
they differ in size somewhat. At temperatures above 106, the
present exhibits a second peak which, although not present
in the tabulation of Mohan et al. (1990), does show when
we thermally average their collision strength from the QUB atomic databank.
We conclude that Mohan et al. (1990) may have truncated the integration
over energy too soon when calculating .
Figure 16: 
: a)
Mohan et al. (1990); b) IRON Project