# Benchmark calculations for electron-impact excitation of Mg$^{4+}$

## TL;DR

This study compares different computational methods for electron-impact excitation rates in Mg$^{4+}$, confirming the accuracy of some results and highlighting the importance of target structure representation and convergence in collision data.

## Contribution

It provides an independent BSR calculation with improved target structure and extensive state inclusion, clarifying discrepancies with DARC results and estimating uncertainties in excitation data.

## Key findings

- BSR results agree with previous BSR calculations, confirming their accuracy.
- Discrepancies with DARC are mainly due to structure representation and pseudoresonances.
- Extensive calculations with 316 states improve convergence and uncertainty estimates.

## Abstract

There are major discrepancies between recent B-spline R-matrix (BSR) and Dirac Atomic R-matrix Code (DARC) calculations regarding electron-impact excitation rates for transitions in Mg$^{4+}$, with claims that the DARC calculations are much more accurate. To identify possible reasons for these discrepancies and to estimate the accuracy of the various results, we carried out independent BSR calculations with the same 86 target states as in the previous calculations, but with a different and more accurate representation of the target structure. We find close agreement with the previous BSR results for the majority of transitions, thereby confirming their accuracy. At the same time the differences with the DARC results are much more pronounced. The discrepancies in the final results for the collision strengths are mainly due to differences in the structure description, specifically the inclusion of correlation effects, and due to the likely occurrence of pseudoresonances. To further check the convergence of the predicted collision rates, we carried out even more extensive calculations involving 316 states of Mg$^{4+}$. Extending the close-coupling expansion results in major corrections for transitions involving the higher-lying states and allows us to assess the likely uncertainties in the existing datasets.