# Calculations of Cross-Sections for Positron Scattering on Benzene
## 3 Results and Discussion
The SBP results reach their maximum value of \(2.98\times 10^{-20}\) m\({}^{2}\) at 30 eV. This is much smaller than our results and the IAM-SCAR+I results. It is also important to note that our calculations are for excitation into the excited states \(1^{1}E_{1u}\), \(2^{1}E_{1u}\) and \(1^{1}A_{2u}\). The cross-sections for the excitation of each state are shown in Figure 5. All three states are dipole allowed (the transition dipole moment between the ground state and the excited state is non-zero). [PERSON] studied transitions into \({}^{1}E_{1u}\) and the dipole-forbidden state \({}^{1}B_{1u}\). [PERSON] et al. [26] do not specify the electronic states that they consider in their calculation. Figure 4: Integral cross-sections for positron impact excitation of electronic states in benzene. Present calculations using the BE-scaled Born approximation are shown by the solid red line. Also shown are IAM-SCAR+I results [26] (dashed blue line) and SBP results [27] (green dotted line). Figure 5: Integral cross-sections for positron impact excitation of electronic states in benzene. Present calculations using the BE-scaled Born approximation. In Figure 6, we show our estimate of the total cross-section, excluding the cross-section for Ps formation. \[\sigma_{total-Ps}=\sigma_{el}+\sigma_{ion}+\sigma_{elec}. \tag{12}\]  
Here, we sum the elastic cross-section \(\sigma_{el}\), the cross-section for direct ionization \(\sigma_{ion}\) and the cross-section for electronic excitation \(\sigma_{elec}\). The elastic cross-section is taken from [PERSON] (2007), which is obtained by the R-matrix method with enhancement factors. The ionization cross-section is computed with the BEB-B method and the cross-section for electronic excitation uses the BE-scaled Born approximation. In Figure 6, we present the total cross-sections obtained by the IAM-SCAR+I method ([PERSON] et al., 2010) and experimental results by [PERSON] (2010), [PERSON] et al. (2010), [PERSON] et al. (2010), and [PERSON] et al. (2010, 2011). [PERSON] et al. (2010) calculated corrections for the angular discrimination error in the experiment by [PERSON] et al. (2010) for collision energies below 1 eV. These corrections bring [PERSON]'s results very close to [PERSON]'s results, but are not shown in Figure 6. It should be noted that the results of [PERSON] et al. (2010) are considered too low at collision energies below 50 eV. A detailed discussion about these results can be found in the review by [PERSON] et al. (2014). For energies below 2 eV, the IAM-SCAR+I cross-sections are lower than the experimental cross-sections, whereas for energies larger than 2 eV, they are the largest cross-sections in the figure. The IAM-SCAR+I cross-sections show a maximum around 10 eV, which is absent in all other datasets. [PERSON] et al. (2014) recommend the experimental values from [PERSON] et al. (2010) as the total cross-section for low energies and the values from [PERSON] (2010) for large collision energies. For energies below the threshold for Ps formation and for energies above 30 eV, the sum of our cross-section \(\sigma_{total-Ps}\) is very close to the experimental data points from [PERSON] et al. (2010, 2011) and [PERSON] (2010). In the range between 3 and 30 eV, the sum of our cross-sections is smaller than the recommended cross-section. We assume that this difference is due to Ps formation. For an estimation of the cross-section for Ps formation,  
\[\sigma_{Ps}=\sigma_{total}^{\text{recommended}}-\sigma_{total-Ps}\]  
we subtract the sum \(\sigma_{total-Ps}\) of our cross-sections from the recommended total cross-section \(\sigma_{total}^{\text{recommended}}\) from [PERSON] et al. (2014). The estimated cross-section for Ps formation  
Figure 1:0 Total cross-sections for positron collisions with benzene. Present results are shown by the solid red line. Also shown are results obtained with the IAM-SCAR+I method (dashed blue line) and experimental results by [PERSON] (2010) (black circles), [PERSON] et al. (2010) (blue triangles), [PERSON] et al.