4 Discussion and conclusion

Unlike the lower ionization stages of Fe, such as Fe III and Fe IV, it is found that it is necessary to explicitly consider the fine structure in the target in order to delineate precisely the positions of autoionizing resonances and detailed resonance structures. However the overall relativistic effects on the the Maxwellian-averaged collision strengths are small, and the NR and BPRM approximations yield close agreement for the forbidden transitions between the low-lying even states. Before carrying out the large-scale 34CC calculation, the test runs with the BPRM method (Berrington et al. 1995) using a 19-level target corresponding to the 8 LS terms showed that although the 19BP calculations show significant difference in the positions and shapes for the resonance features in individual transitions, the overall difference in the averaged collision strengths is small among the 19BP, 8CC and 34CC calculations. However, the smaller 8CC or the 19BP calculations entail only a small number of transitions compared to the larger 34CC calculation. Establishing that the relativistic effects are indeed not important for the calculation of the rate coefficients of Fe VI, this provided the basis for the much more extensive calculations. The algebraic recoupling method, following the NR calculations, was used to obtain results for all transitions among the 80 fine structure levels of the 34 LS terms.

Here, we give an estimate of the accuracy of the present data. An examination of Tables 2nd 3 suggests that the general level of agreement between the 3 sets of results may be used as an accuracy criterion, indicating the maximum dispersion due to numerical uncertainties associated with resolution of resonances and relativistic effects to the extent they are operative. The fine mesh was used up to E = 0.7 Ry and the important resonance features for transitions from the lower-lying, even-parity levels up to the $\rm 3{\rm d}^3\ ^2D1^{\rm o}_J$ levels are fully resolved so rate coefficients for this type of transitions should be highly accurate, $\approx 10-20$%. For optically allowed transitions from the low-lying levels to the odd parity levels with energies below 0.7 Ry, the rate coefficients should also be of the same accuracy since resonances are relatively less important and the collision strengths are large and dominated by the higher partial waves, as seen from Fig. 3. For the other forbidden (and inter-combination) transitions between these intermediate-energy levels, the accuracy of the rate coefficients is expected to be less, $\approx 30-50$%. For transitions corresponding to excitation to the high-lying levels with threshold energies greater than 2.8 Ry, the uncertainty could exceed 50% since a coarse energy mesh was used and the resonances and coupling effects due to higher terms were neglected. We would also emphasize here that for all transitions the Maxwellian-averaged collision strengths for high temperatures (roughly higher than the highest threshold energy included in the target expansion, about 400 000 K in the present case) could have a larger uncertainty, since resonances due to higher target states are not included. However, data at temperatures much higher than these are of little astrophysical interest. This general criterion should apply to all our earlier publications in this series.

The present work will hopefully provide a reasonably complete collisional dataset for extensive astrophysical diagnostics of Fe VI spectra from various sources. Further work is planned on the forbidden transition probabilities of [Fe VI], and on computation of line ratios using the collisional and radiative datasets. An electronic data table of all the non-vanishing Maxwellian-averaged collision strengths between the 80 fine structure levels constitutes Table 4 of the present work. As Table 4 is rather voluminous it is available in electronic form from the CDS or via ftp from the authors at: chen@astronomy.ohio-state.edu.

Acknowledgements

We wish to thank Dr. Manuel Bautista for his contribution in obtaining the target wave functions, and Prof. Keith Berrington for the analysis of bound channel resonances. This work was supported by a grant (AST-9870089) from the U.S. National Science Foundation and by NASA grant NAG5-6908. The calculations were carried out on the massively parallel Cray T3E and the vector processor Cray T94 at the Ohio Supercomputer Center in Columbus, Ohio.