Previous calculations of collision strengths for the 3s23p33s3p4 electric dipole transitions in FeXII by F77 and TH88 are available for a detailed comparison with the present results.
F77 adopted a distorted wave approach coupled with a limited target model including 4 configurations (3s23p3, 3s3p4, 3s23p23d and 3p5), and computed collision strengths at only one value of energy (6.6Ry). Due to the approximation used in the scattering process and to limitations in computational resources, resonance effects and the variation of with E could not be explored. In Table 4 we compare the two sets of data by choosing a cut-off of of the present results. Values in F77 which do not agree within with our collision strengths have been denoted with the superscript a. Out of 35 transitions, 6 () do not satisfy the criterion and have not been included in the analysis. It should be noted that of these 6 transitions only 1 has in our calculation. For the remaining 29 transitions we find an average difference of from our results.
TH88 adopted a more comprehensive target representation, also including correlation orbitals, and used the more sophisticated R-matrix approach in their scattering calculation. Details of their computation have been extensively discussed in relation to ours in BMS. We compare the two sets of collision strengths in Table 4 at the lowest (6.6Ry) and highest (30Ry) energies for which they tabulate values. At 6.6Ry 10 transitions () do not satisfy the criterion and we find an average difference of from our data for the remaining values. It is important to note that all the 's excluded are in our computation. At 30Ry we find an average difference of from our data, after exclusion of 9 transitions (), of which only 1 has in our set. A comparison over the entire energy range tabulated by TH88 reveals that the two sets of 's have the same trend as a function of E.
We stress the point that all the collision strength values which show the most severe disagreement between the different sets of calculations, up to more than an order of magnitude in some cases, are "weak'' transitions, i.e. transitions with . For these transitions the strong mixing of levels and consequent cancellation effects in the matrix elements, which depend on the particular choice of the target model, are more likely to introduce big discrepancies in the collision strengths, as shown by the above analysis. This shows once more the importance of a proper choice of target representation in a scattering calculation, i.e. one in which full account is taken of interaction effects between configurations of a parity complex.
As is the case for the forbidden transitions within the 3s23p3 ground configuration (Tayal et al. 1987), a large discontinuity between the values at 4Ry and at 6.6Ry is evident in TH88 electric dipole collision strengths. As discussed in BMS, this is likely to be due to residual pseudo-resonance effects in the open channel energy region and, because of this, it should not be surprising that our collision strengths at 6.6Ry agree marginally better with F77, despite the more sophisticated approach adopted in the present work and by TH88.
The problems introduced by these non-physical pseudo-resonances in the
open channel energy region and by the extra resonances below the
highest excitation threshold, brought in by orbitals of correlation
type, show up even more drastically in the effective collision
strengths. A comparison between our results , tabulated in Table 6,
and TH88 can be made in the range 4105K - 3106K.
The two sets of effective collision strengths have the
same trend as a function of , with the noticeable exception of
the 6 transitions marked by the superscript b in Table 6. For
these transitions our
's increase with , whereas 's in TH88
fall off with , which is surprising considering that
these are all optically allowed transitions and, most importantly,
that for both sets of calculations the corresponding 's
increase with E above 6.6Ry. The large drop in between
4Ry and 6.6Ry, mentioned above, almost certainly accounts for this
unusual behaviour resulting from the integration of
the collision strengths over a Maxwellian function. Further support for
this hypothesis is offered by the 3s23p3
2P 3s3p4 2S1/2
(c in Table 6), which in TH88
shows a drop of almost a factor of 2 in the
collision strength between 4Ry and 6.6Ry (their Table 2).
This is clearly reflected in the drop of the effective collision strength at
the lowest three temperatures tabulated in their Table 3. Starting
from K onwards the expected increase of with
is otherwise correctly reproduced. If we make a numerical
comparison of the two sets of data, we find that (at
4105K) and (at 3106K) of transitions differ by
more than , as shown by a superscript a in Table 6. We
also note that for all such transitions (present
work)<(TH88). This, along with the fact
that significantly more transitions have been rejected at the lower
, where resonance effects are more likely to contribute in the
integration, forces us to believe once more that the reason for the
large values in TH88 lies in pseudo-resonance contributions
due to the use of correlation orbitals in the target description.
The transitions marked by b in Table 5 deserve a separate discussion as we have evidence of label misassignment for the upper levels of these transitions in F77. The most striking case is for the two levels (3P)2F5/2 and (3P)2D5/2. By comparing the collision strength values for 2D - (3P)2F5/2 and 2D - (3P)2D5/2 in Table 5 it is evident that the relative strengths of these two transitions are reversed in the two calculations. By reassigning in F77 the higher collision strength to the former transition and the lower one to the latter we get a significant improvement in agreement from more than 2 orders of magnitude down to and (still a big difference, but this is a low value, !), respectively. Similarly for the 2P - (3P)2F5/2, 2P - (3P)2D5/2 transitions by interchanging the collision strengths in F77 the difference between the two sets of data drops from more than 2 orders of magnitude down to and respectively. The other suspected case of mislabelling is that of levels (1D)2P1/2 and (1D)2S1/2. The stronger transition in our computation is the 2P - (1D)2S1/2 rather than the 2P - (1D)2P1/2 as in F77. By reassigning the high to the former transition in F77, the difference decreases from more than a factor of 4 down to . Similarly, by interchanging the 's for the 2P- (1D)2P1/2, 2P - (1D)2S1/2 transitions in F77, we get a difference of for the stronger 2P - (1D)2P1/2 transition, against a difference of more than a factor of 2 shown in Table 5. In F77 it is clearly stated that, due to the neglect of excited configurations of the even parity complex, the wavefunctions of some of the 3s23p23d excited states might be substantially wrong in that work. The strong mixing of the levels mentioned above depends critically on the target basis expansion and we propose that the mislabelling affecting the F77 data might be due to his use of an incomplete target basis set.
One last point of discussion concerns the assignment of observed energy values in F77. In that work experimental energies are derived from transition wavelengths given in Fawcett (1971), who provided data for the (1D)2D term but not for the (1S)2D term. In our calculation (see Table 1) the (1S)2D levels are energetically lower than the (1D)2D levels but F77 seems to suggest a reversed ordering in his listing, despite the lack of any clear indication of term parentages. A SUPERSTRUCTURE calculation with only 4 configurations in the basis set, performed to mimic the F77 atomic model, revealed that the (1D)2D levels are indeed still energetically higher than the (1S)2D levels, providing a clue to a possible misassignment in F77. By reassigning the 553855 cm-1 and 554575 cm-1 observed energies to the second lowest 3s23p23d2D doublet in his Table 1 we would get proper agreement with our results and with the updated observed energies by Corliss Sugar (1982).
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