5 Discussion and conclusion

An extensive calculation of fine structure transition probabilities of Fe VI is presented for the allowed E1 and the forbidden E2, M1 transitions. An indication of the uncertainties in the computed gf-values is given in the plot of length $gf_{\rm L}$ vs. the velocity $gf_{\rm V}$for 867 E1 transitions computed in this work (Fig. 7).

It shows an agreement at about 10% level for most of the transitions, with no more than about 5% of the transitions lying outside that range even for gf-values less than 10^-4.

Combined with previously calculated data for electron impact excitation, a 80-level CR spectral model for line ratios diagnostics is used to predict the effect of collisional and fluorescent excitation (FLE) in planetary nebulae. An illustrative and limited analysis of line ratios is carried out as an example of the use of the atomic data and the model proposed herein. Some of the diagnostics procedures developed earlier by Chen & Pradhan (2000, CP00) are employed to analyse observed line intensties from three planetary nebulae: NGC 6741, IC 351 and NGC 7662. The analysis aims at a consistent set of diagnostics, for example, for the electron density and effective temperature of the source. It shows that fluorescence effects should be included in CR models of these objects. An estimate is made of both the temperature and the emission region distance (via a dilution factor) for the PN IC 351. By combining the line ratios that are independent of the physical conditions of PNe (like cases in Table 5), and our method, one could estimate possible observational errors individually and in term of consistency among sets of observed lines. It is expected that the method and procedures described in this paper would be generally applicable to spectral diagnostis of other radiative plasma sources, such as novae and AGN.

The luminosity and distance of the source determines the local density of photons and the efficacy of FLE to compete with collisional excitation. For complex iron ions with many affected transitions, the extension of the standard line ratios analysis to include FLE requires a number of line ratios in order to derive a self-consistent set of parameters that explain the observed line fluxes and ratios.

Finally, some possible uncertainties may be due to following assumptions: 1) static conditions in the CR model, independent of photoionization equilibrium; 2) constant $N_{\rm e}$ and $T_{\rm e}$ in [Fe VI] emission regions (but which may vary with distance to the central star); 3) the radiation field is Planckian, and not a realistic ionizing stellar radiation. A further refinement of the model proposed herein would be (a) to include a radiation field with proper allowance for the Helium and Hydrogen opacities in various ionization and excitation steps, and (b) in addition to the radiation flux from the central star, resonance fluorescence from H I and He II Ly$\alpha$ should be considered in the model. However as noted earlier, Fe VI is likely to be in the fully ionized He III zone, and therefore not greatly susceptible to these effects. Even though the most advanced R-matrix codes are employed in generating atomic data, the atomic data still have some uncertainties, estimated at about 10 - 20%.

All data tables are available electronically from the CDS, or via ftp from the authors at: chen@astronomy.ohio-state.edu.

Acknowledgements

This work was supported by a grant (AST-987008) from the U.S. National Science Foundation and by NASA grant NAG5-7903. 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.