On the use of the Axelrod formula for thermal electron collisions in astrophysical modelling

The Axelrod approximation is widely used in astrophysical modelling codes to evaluate electron-impact excitation effective collision strengths for forbidden transitions. Approximate methods such as this are a necessity for many heavy elements with open shells where collisional data is either non existent or sparse as the use of more robust methods prove prohibitively expensive. Atomic data for such forbidden transitions are essential for producing full collisional radiative models that do not assume Local-Thermodynamic-Equilibrium (LTE). In this short work we present the re-optimization the simple Axelrod formula for a large number of R-matrix data sets, ranging from Fe and Ni to the first r-process peak elements of Sr, Y and Zr, to higher Z systems Te, W, Pt and Au. We show that the approximate treatment of forbidden transitions can be a significant source of inaccuracy in such collisional radiative models. We find a large variance of the optimized coefficients for differing systems and charge states, although some general trends can be seen based on the orbital structure of the ground-state-configurations. These trends could potentially inform better estimates for future calculations for elements where R-matrix data is not available.