Validity of the ICFT R-matrix method: Be-like Al 9+ a case study

Abstract

We have carried-out 98-level configuration-interaction / close-coupling (CI/CC) intermediate coupling frame transformation (ICFT) and Breit-Pauli R-matrix calculations for the electron-impact excitation of Be-like Al 9+ . The close agreement that we find between the two sets of effective collision strengths demonstrates the continued robustness of the ICFT method. On the other hand, a comparison of this data with previous 238-level CI/CC ICFT effective collision strengths shows that the results for excitation up to n = 4 levels are systematically and increasingly underestimated over a wide range of temperatures by R-matrix calculations whose close-coupling expansion extends only to n = 4 (98-levels).Thus, we find to be false a recent conjecture that the ICFT approach may not be completely robust. The conjecture was based upon a comparison of 98-level CI/CC Dirac R-matrix effective collision strengths for Al 9+ with those from the 238-level CI/CC ICFT R-matrix calculations. The disagreement found recently is due to a lack of convergence of the closecoupling expansion in the 98-level CI/CC Dirac work. The earlier 238-level CI/CC ICFT work has a superior target to the 98-level CI/CC Dirac one and provides more accurate atomic data.Similar considerations need to be made for other Be-like ions and for other sequences.

Discrepancies in Atomic Data and Suggestions for Their Resolutions

“…Since in a majority of cases Υ ICF T were greater than Υ DARC -particularly see fig. 2 of [61] -it appears to be a sound reason, as discussed and demonstrated in a series of papers by Badnell and co-workers [62,63,64]. Below we elaborate more on the differences between the DARC and ICFT calculations.…”

“…1(b). For this ion the reasoning of a larger model given by [62] and shown in their fig. 2 appears to be plausible.…”

Scaling of collision strengths for highly-excited states of ions of the H- and He-like sequences

“…Clearly, it is first necessary to have a good starting calculation before applying the extrapolations to the data. We note that R-matrix results become increasingly uncertain for the highest energy states included in the CI and CC expansions of the target, due to their lack of convergence (Fernández-Menchero et al 2015). The description of the atomic structure, energy levels and radiative data, and the corresponding effective collision strengths, increasingly lose accuracy as we approach the last states included in the basis expansions.…”

Energy levels, radiative rates and electron impact excitation rates for transitions in Si III

“…The error in the code was later rectified by [20]. Moreover, in certain circumstances the ICFT approach does lead to the overestimation in the ϒ values, as discussed by [21] for transitions in O III, and also explained by [10]. Nevertheless, in this paper we consider the results for Si III, which is not only an important Mg-like ion but its atomic data have recently been 'benchmarked' by [22].…”

“…However, in a series of papers [10][11][12] the overestimation of ϒ results with the ICFT methodology has been justified on the basis of the larger calculations performed by the group authors. For example, we included only 98 levels of the 2 2 , 2 3 and 2 4 configurations for most Be-like ions [6,[13][14][15], and only 166 for C III [7], the additional 68 levels belonging to the 2 5 configurations, well short of 238 considered by [16].…”