# Extension of the Discrete Electron Transport Capabilities of the Geant4-DNA Toolkit to MeV Energies
## 3 Results and Discussion  
### Inelastic Cross Sections  
In Figure 2, we present calculated cross sections in the energy range from threshold up to 10 MeV for each ionization shell and excitation level using the present model (DNA-Opt4X). The cross sections exhibit the typical behavior of a rapid increase above the threshold energy of each inelastic channel and a subsequent decrease, due to the inverse proportionality to the square of the electron velocity, up to about the electron rest mass energy (\(\sim\)500 keV) where relativistic effects set in. At even higher energies, the so-called relativistic rise may be observed (practically above \(\sim\)1 MeV). As expected, above a few tens of eV ionization cross sections become larger than the excitation cross sections. This is a direct consequence of the underlying ELF model which uses ordinary and derivative Drude functions (the latter decreasing more rapidly with energy) to model the ionization and excitation transitions, respectively. In Figure 3, we show separately the longitudinal and transverse inelastic TCS terms for the individual ionization shells (top panel) and excitation levels (bottom panel) over the energy range from 100 keV to 10 MeV. Note that the ionization cross sections for shells \(j\) = 1 and \(j\) = 2 (for both the longitudinal and transverse terms) are indistinguishable in Figure 2 (top panel) due to the log scale. Note that the onset of the transverse contribution is set at energies above 100 keV according to the 1% criterion (see Figure 1). The same trend is observed for both the excitation and ionization cross sections as a function of electron energy; namely, the rapid decrease in the longitudinal contribution becomes more gradual for energies above the electron rest mass, whereas the transverse contribution steadily increases throughout the entire energy range. The combined effect leads to the relativistic rise observed in Figure 2.  
Figure 3: The longitudinal and transverse contribution to the electron inelastic cross section for each outer ionization shell (**top** panel) and excitation level (**bottom** panel) of liquid water in the energy range from 100 keV to 10 MeV calculated by the present model (DNA-Opt4X). Figure 2: Electron inelastic cross sections for each (outer) ionization shell (\(j\) = 1–4) and excitation level (\(k\) = 1–5) of liquid water in the energy range from threshold (\(\sim\)10 eV) to 10 MeV calculated by the present model (DNA-Opt4X). The relative magnitude of the longitudinal and transverse contribution to the total inelastic cross section is shown in Figure 4. It can be seen that the transverse contribution is \(\sim\)1% at 100 keV, \(\sim\)2% at 200 keV, \(\sim\)10% at 1 MeV, and \(\sim\)30% at 10 MeV. Thus, when extending MCTS simulations to electron energies beyond a few hundred keV (and especially beyond 1 MeV), the inclusion of the transverse term of the inelastic cross section is necessary so as to avoid a significant (and systematic) overestimation of the inelastic mean free path. Figure 5 shows a comparison of the total ionization (top panel) and total excitation (bottom panel) cross section between DNA-Opt2, which extends up to 1 MeV, the present model (DNA-Opt4X), which extends up to 10 MeV, and DNA-Opt6 which extends up to 256 keV. The differences at low energies are discussed elsewhere [43; 44]. In brief, the differences between the two dielectric-based inelastic models (i.e., those of DNA-Opt2 and DNA-Opt4X) are due to the different ELF algorithms and the different implementations of the low-energy Mott-Coulomb corrections. These differences yield ionization cross sections which differ by up to \(\sim\)50% at sub-100 eV energies but less than \(\sim\)10% above \(\sim\)100 eV. On the other hand, the ionization cross sections of DNA-Opt6, which are calculated by the Binary-Encounter-Bethe (BEB) model [45], are consistently higher, especially for sub-100 eV energies. This is mainly due to the neglect of long-range screening effects in the BEB (being essentially an atomic model).