## 3 Results  
### Demonstration of Monoenergetic Collision Cross Sections  
The results section starts here with demonstrations of the published discrete-points monoenergetic collision cross sections corresponding to method 3, along with the weight function for each of the six species covered herein. Although this part is not the main outcome of the present study, it is still considered very helpful in explaining the influence of the electron temperature and the electrons' monoenergetic thermal speed (thus, the electrons' monoenergetic kinetic energy) on the predicted simplified speed-independent electron-neutral collision cross sections. Figure 1 shows a graphical representation of the tabulated data of the monoenergetic (speed-dependent) electron-neutral collision cross sections (\(Q\)) for carbon monoxide (CO). The figure combines this graphical representation of the collision cross sections with another graphical representation for the corresponding weight function (\(g\)), which was computed here after the value of the non-dimensional energy ratio (\(x\)) was deduced for each of the published values of the electron kinetic energy (\(u_{e}\)). For each of the six gaseous species, the monoenergetic collision cross sections are strictly dependent on the electron monoenergetic thermal speed (\(v_{e}\)) or, equivalently, on the related electron monoenergetic kinetic energy (\(u_{e}\)). However, these monoenergetic collision cross sections can also be viewed as a function of the non-dimensional energy ratio (\(x\)) but for a given electron absolute temperature (\(T_{e}\)). Thus, three scales are used in the horizontal axis in the figure, such that each of these three variables can be utilized as the independent variable for \(Q\). In the first (top) plot of the figure, \(T_{e}\) = 2000 K. This parameter is necessary to determine the value of \(x\) at each value of \(u_{e}\) or \(v_{e}\). In the second (bottom) plot of the figure, the \(x\) values are inferred from the \(u_{e}\) or \(v_{e}\) values with a higher parameter value of \(T_{e}\) = 3000 K. The change in \(T_{e}\) does not impact the profile of \(Q(u_{e})\) or \(Q(v_{e})\) because these profiles are temperature-invariant. Instead, the increase in \(T_{e}\) only impacts the profile of \(g(u_{e};T_{e})\) or \(g(v_{e};T_{e})\) by stretching the profile of \(g\) horizontally along the horizontal \(u_{e}\) axis or the horizontal \(v_{e}\) axis, respectively. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Index** & **Species** & **Correlation** \\ \hline
1 & CO & \(\overline{Q}=5.523+0.001913\ T_{e}\) \\ \hline
2 & CO\({}_{2}\) & \(\overline{Q}=79.82-0.02871\ T_{e}+3.148\times 10^{-6}\ T_{e}^{2}\) \\ \hline
3 & H\({}_{2}\) & \(\overline{Q}=9.410+0.001287\ T_{e}-6.578\times 10^{-8}\ T_{e}^{2}\) \\ \hline
4 & H\({}_{2}\)O & \(\overline{Q}=406.6-0.1842\ T_{e}+2.533\times 10^{-5}\ T_{e}^{2}\) \\ \hline
5 & K & \(\overline{Q}=958.2-0.3434\ T_{e}+4.291\times 10^{-5}\ T_{e}^{2}\) \\ \hline
6 & O\({}_{2}\) & \(\overline{Q}=2.569+6.473\times 10^{-4}\ T_{e}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Recommended correlations for the average electron–neutral collision cross section (\(\overline{Q}\), in Å\({}^{2}\)) in the fourth method as a function of the electron absolute temperature (\(T_{e}\), in K). Despite this, the profile of \(g(x)\) is the same in both plots, because the relation between \(g\) and \(x\) is temperature-invariant, as previously shown in Equation (32). The figure illustrates the role of \(T_{e}\) in broadening the profile of \(g(u_{e};T_{e})\) or \(g(v_{e};T_{e})\) relative to the static profile of \(Q(u_{e})\) or \(Q(v_{e})\), leading to different integration results due to the deformation in the weight function, not due to a change in the monoenergetic collision cross section function. The original data were published for a range of monoenergetic electron kinetic energy (\(u_{e}\)) values from 0.0005 eV to 6.000 eV.