# Calculations of Cross-Sections for Positron Scattering on Benzene
## 3 Results and Discussion  
In Figure 1, we present the cross-sections for the direct ionization of the benzene molecule by positron impact and compare them with available results from the literature. The figure shows the computed ionization cross-section, which is obtained with the four BEB models and the calculations by [PERSON] et al. [26] using the independent atom model with the screening-corrected additivity rule including interference effects (IAM-SCAR+I) method. From Figure 1, it can be seen that for collision energies below 40 eV, the IAM-SCAR+I method gives the largest cross-section. The results, obtained with the four BEB models, are relatively close together, where BEB-0 gives the largest cross-sections, followed by BEB-W, BEB-B, and BEB-A. The IAM-SCAR+I reaches a maximum at 40 eV. In contrast, BEB-0 has its maximum at 59 eV, BEB-W at 63 eV, BEB-A at 71 eV, and BEB-B at 72 eV. For collision energies above 200 eV, all four BEB curves converge, and the lines are not distinguishable in Figure 1 and are slightly above the IAM-SCAR+I curve. In our previous study of positron impact ionization, we obtained the best results for neutral molecules with the BEB-A and BEB-B models. Therefore, we will use the BEB-B results in our calculation of the TCS. In Figure 2, we show the cross-sections for the direct ionization for each valence orbital. For the computations, we used the BEB-B model. We can see that the largest contribution is due to the highest molecular orbital. In Figure 3, we show the contributions of the four core orbitals. The cross-sections for each of the four core orbitals are below \(0.01\times 10^{-20}\) m\({}^{2}\) \begin{table}
\begin{tabular}{c c c c} \hline
**Excited State \(Y\)** & **Description** & \(f_{0Y}\) & \(\Delta E\)**/eV** \\ \hline \(1^{1}E_{1u}\) & [PERSON] \(\pi\rightarrow\pi^{*}\) & 0.2021 & 7.06 \\ \(2^{1}E_{1u}\) & Valence \(\pi\rightarrow\pi^{*}\) & 0.6204 & 7.48 \\ \(1^{1}A_{2u}\) & [PERSON] \(\pi\rightarrow\sigma^{*}\) & 0.0350 & 7.06 \\ \hline \end{tabular}
\end{table} 
Table 2: Electronically excited states of benzene with non-zero oscillator strength. All states have been computed using SAC-CI by [PERSON] et al. [45]. The parameters \(B_{i}\) and \(U_{i}\) are the same for all four orbitals. Due to the degeneracy of the orbitals \(1e_{1u}\) and \(1e_{2g}\), their cross-sections are two times larger than the cross-sections for the ionization from the orbitals \(1b_{1u}\) and \(1a_{1g}\). Figure 1: Direct ionization cross-section from benzene molecules by positron impact. The results from calculations with the four different BEB models are shown by a solid red line (BEB-0), dashed red line (BEB-W), dotted red line (BEB-A), and dash–dotted red line (BEB-B). The data from calculations by [PERSON] et al. [26] with the IAM-SCAR+I method are shown by the dashed blue line. Figure 3: Direct ionization cross-section from benzene molecules by positron impact for the core orbitals computed with the BEB-B model. The cross-sections for the orbitals \(1e_{1u}\) and \(1e_{2g}\) cannot be distinguished from each other. The same applies for the orbitals \(1b_{1u}\) and \(1a_{1g}\). Figure 2: Direct ionization cross-section from benzene molecules by positron impact for the valence orbitals computed with the BEB-B model. Regarding the electronic excitations of benzene by positron impact, calculations have been performed by [PERSON] et al. [26] using the IAM-SCAR+I method and by [PERSON] [27] using the scaling Born positron (SBP) approach. Figure 4 shows our results using the BE-scaled Born approximation together with the results of the IAM-SCAR+I method [26] and the SBP approach [27]. The curve with BE-scaled cross-sections reaches a maximum of \(6.92\times 10^{-20}\) m\({}^{2}\) at 15 eV. The IAM-SCAR+I results show a maximum value of \(15.26\times 10^{-20}\) m\({}^{2}\) at the same energy and are larger than our results for nearly all collision energies, with the exception of a small energy range between 30 and 60 eV.