Importance of the completeness of the configuration interaction and close coupling expansions in R-matrix calculations for highly-charged ions: electron-impact excitation of Fe $^{20+}$

Abstract: We have carried-out two intermediate coupling frame transformation (ICFT) R-matrix calculations for the electron-impact excitation of C-like Fe $^{20+}$, both of which use the same expansions for their configuration interaction (CI) and close-coupling (CC) representations. The first expansion arises from the configurations 2s$^2$ 2p$^2$, 2s 2p$^3$, 2p$^4$, {2s$^2$ 2p, 2s 2p$^2$, 2p$^3$} nl, with n=3,4, for l=0-3, which give rise to 564 CI/CC levels. The second adds configurations 2s$^2$ 2p 5l, for l=0-2, which give rise to 590 CI/CC levels in total. Comparison of oscillator strengths and effective collision strengths from these two calculations demonstrates the lack of convergence in data for n=4 from the smaller one. Comparison of results for the 564 CI/CC level calculation with an earlier ICFT R-matrix calculation which used the exact same CI expansion but truncated the CC expansion to only 200 levels demonstrates the lack of convergence of the earlier data, particularly for n=3 levels. Also, we find that the results of our 590 CC R-matrix calculation are significantly and systematically larger than those of an earlier comparable Distorted Wave-plus-resonances calculation. Thus, it is important still to take note of the (lack of) convergence in both atomic structural and collisional data, even in such a highly-charged ion as Fe $^{20+}$, and to treat resonances non-perturbatively. This is of particular importance for Fe ions given their importance in the spectroscopic diagnostic modelling of astrophysical plasmas.