4 Results

Since previous work by CNP, BMB and BM was mainly concerned with the computing of collision strengths, we have made fairly extensive comparisons in terms of this quantity in an attempt to assign an accurate rating to the present effective collision strength dataset. Following BM, we compare collision strengths at the incident electron energy of 50 Ryd (Table 4). In general it is found that present data are slightly larger than those by BM, BMB and CNP, in particular for transitions with small collision strengths; this seems to indicate that the partial wave convergence of the present dataset has been accomplished more thoroughly. Nonetheless the agreement of BM and CNP with the present dataset is very reasonable as 84% of the transitions agree to better than 20%. Larger differences are found with BMB where this level of agreement is only met by 76% of the compared transitions. Further comparisons with the work by BM is not possible as they do not list collision strengths at other energies.

  

Figure 1: Collision strength plotted in the reduced scale of Burgess & Tully (1992) for the quadrupole transitions a) 3s$^2\,^1$S0-3s3d$\,^1$D2 and b) 3p$^2\,^1$D2-3s3d$\,^1$D2. Solid line, present results; squares, BMB; crosses, CNP. The significant discrepancies found with respect to present results are believed to be caused by the neglect of the contributions from high partial waves

Differences with the datasets by CNP and BMB arise due to partial wave convergence problems that show up mainly in the quadrupole transitions. This situation is clearly illustrated in Fig. 1. BMB have taken into account the contributions from $12\leq l\leq 40$ with the non-exchange package NELMA (Cornille et al. 1992) only for transitions arising from the ground level. Therefore the agreement is satisfactory for transition 1-14 (3s$^2\,^1$S₀-3s3d$\,^1$D₂) but discrepant by a factor of $\sim$2 for transition 7-14 (3p$^2\,^1$D₂-3s3d$\,^1$D₂). For the same reason, an even bigger difference of a factor of one hundred is noted for transition 6-12 whose collision strength happens to be small. Since CNP neglected contributions from l>11 for all non-dipole transitions, discrepancies are encountered in all three cases. Similar differences (38%) are also found with the values quoted by CNP for the quadrupole transitions 10-14 and, to a lesser extent (<25%), 1-7, 1-9 and 7-10 (see Table 4).

  

Figure 2: Reduced collision strength for the 3s3p$\,^3$P$^{\rm o}_1-3$p$^2\,^1$S0 intercombination transition. Solid line: present results. Squares: BMB. Crosses: CNP. Filled circle: high-energy limit. The discrepancies found between BMB and present results are probably due to a poorly represented 3p$^2\,^1$S0 in the former work

Noticeable differences are also found with the collision strengths calculated by BMB for some transitions involving the 3p$^2\,^1$S₀ level, which in their case, as discussed above, is poorly represented due to the exclusion of correlation from the 3d² configuration. In Fig. 2 the present collision strength for the 3s3p$\,^3$P$^{\rm o}_1-3$p$^2\,^1$S₀ intercombination transition is plotted using the reduced scale of Burgess & Tully (1992), which shows the correct approach of its high-energy tail towards $\Omega_{\rm r}(1)$; a discrepancy with BMB of $\sim$40% can be seen. A similar problem is also found for the transition 3p$^2\,^3$P₂-3p$^2\,^1$S₀.

  

Figure 3: Reduced collision strength for the 3s$^2\,^1$S0-3p3d$\,^1$P$^{\rm o}_1$ allowed transition. Solid line, present results; squares, BMB; filled circle, high-energy limit. The discrepancies with BMB are due to a small and correlation sensitive gf-value for this transition (see Table 3)

In Fig. 3 we plot the present reduced collision strength for the 3s$^2\,^1$S₀-3p3d$\,^1$P$^{\rm o}_1$ allowed transition which is in substantial disagreement with BMB. The source of this problem is linked to the large difference in the gf-values (a factor of 4) for this transition (see Table 3). By running several structure calculations, it is found that the gf-value for this transition is sensitive to configuration interaction (see Table 3); a more precise gf-value is probably not as large as that listed by BMB but certainly considerably higher than the present. Thus we would not expect our effective collision strengths for this weak transition to be more accurate than a factor of 2. A similar but less pronounced ($\sim 30$%) effect is also found in the case of the 3s3p$\,^1$P$^{\rm o}_1-3$p$^2\,^3$P₀ intercombination transition.

  

Figure 4: a) Reduced collision strength for the 3s$^2\,^1$S0-3s3p$\,^3$P$^{\rm o}_1$ intercombination transition showing the complicated resonance structure. Solid line: present results. Filled circle, high-energy limit. b) Effective collision strength as a function of electron temperature for this transition. Circles: present results. The results by BMB (squares) and CNP (crosses) are also included, which help to denote the large rate enhancement at the lower temperatures caused by the resonance contribution

Effective collision strengths for all the transitions with-in the present Fexv target in the electron-temperature range 10⁵-10⁷ K are tabulated in Table 5. An effect that will influence the rates for some transitions with small backgrounds, e.g. the 3s$^2\,^1$S₀-3s3p$\,^3$P$^{\rm o}_1$ intercombination transition, is depicted in Fig. 4. While the tail of the present reduced collision strength displays the correct approach towards the small high-energy limit and is in good agreement with BMB and CNP, the low-energy regime is dominated by the resonance structure (Fig. 4a). By fitting the collision strengths of BMB and CNP to straight lines and estimating effective collision strengths, it is shown in Fig. 4b that the resonance contribution causes a large enhancement in the present results that is conspicuous even at fairly high temperatures; at an electron temperature of T=10⁶K present rates are 40% higher than both BMB and CNP increasing to a factor of 4 at T=10⁵K. This sort of sizable increases due to resonances in some transitions in the solar temperature range justifies the use of the computationally involved close-coupling approximation for highly ionised ions such as Fexv. This statement is further supported by a comparison of the present effective collision strengths with those listed by Pradhan (1988) estimated from the data by CNP. It is found that only 30% of his data agree with the present ones to within 20%.