# Extension of the Discrete Electron Transport Capabilities of the Geant4-DNA Toolkit to MeV Energies
## 3 Results and Discussion
### Stopping Power Simulations  
Figure 6 (top panel) compares the electronic stopping power (hereafter SP) calculated by 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. SP values from ICRU Report 90 (which is the most recent ICRU Report on the subject) are also depicted [59]. The simulated SP data have been obtained by the Geant4 example called _spower_[17], which transports the particle in frozen velocity mode. Importantly, in the present context, the SP results depend solely upon the ionization and excitation cross sections implemented into the code (i.e., they are not influenced by the elastic model contained in the corresponding constructors). The statistical uncertainty of the SP data presented is less than 1%. It should be noted that the simulated SP data by the different Geant4-DNA constructors (DNA-Opt2, DNA-Opt4X, DNA-Opt6) are essentially equivalent to the numerical calculation of SP  
Figure 5: Comparison of the total ionization cross section (**top** panel) and the total excitation cross section (**bottom** panel) of liquid water as a function of electron energy calculated by different Geant4-DNA constructors, namely, DNA-Opt2 (default), DNA-Opt4X (present/new), and DNA-Opt6. Note that each constructor has a different upper energy limit of application (see text). through Equation (14) using the ionization DCS and excitation TCS of the corresponding constructor. In the bottom panel of Figure 6, the percentage difference in the simulated SP data of each constructor (i.e., inelastic model), from the ICRU values is presented, i.e., \(100\times\frac{\text{SP}_{\text{Landau}}-\text{SP}_{\text{ICRU}}}{\text{SP}_{ \text{ICRU}}}\). The comparison is limited to the ICRU energy range from 1 keV to 10 MeV. Traditionally, ICRU does not provide SP values for electrons at sub-keV energies due to the limitations of the Bethe formula upon which they are based. Specifically, the Bethe SP formula neglects inner-shell corrections and effects beyond the first Born approximation (apart from a kinematic upper cutoff energy limit to knock-on electrons due to indistinguishability). These effects become gradually significant below a few keV. Therefore, the uncertainty of ICRU's SP values is rapidly increasing below 10 keV. In our calculation scheme, inner-shell corrections are automatically included via the dispersion relations that extend ELF to non-zero \(q\), while non-Born effects are included ad hoc through the Mott-Coulomb terms (in addition to the kinematic limit due to indistinguishability). It can be seen that the present model (DNA-Opt4X), not only extends the application of Geant4-DNA to higher energies, namely up to 10 MeV (compared to the 1 MeV upper limit of DNA-Opt2 and 256 keV of DNA-Opt6), but also offers much better agreement with the SP values of ICRU Report 90 [59]. Specifically, in the energy range from 10 keV to 10 MeV, where the ICRU values are most reliable (with reported uncertainty at the \(\sim\)1% level), the present model (DNA-Opt4X) deviates by up to \(\sim\)3%. In the low energy range of 1-10 keV,  
Figure 6: (**Top** panel) Electronic stopping power (SP) of liquid water for electrons over the energy range from 20 eV to 10 MeV simulated by different Geant4-DNA constructors, namely, DNA-Opt2 (default), DNA-Opt4X (present/new), and DNA-Opt6, and compared against the SP values of ICRU Report 90 [59]. (**Bottom** panel) Percentage difference in the various Geant4-DNA constructors from ICRU [59]. the deviation of DNA-Opt4X from ICRU is between 1 and 5%, which roughly coincides with the reported uncertainty range of the ICRU values [59]. It is noteworthy that the deviation of DNA-Opt2 from ICRU is consistently higher than the present model, reaching up to 10% at both the low and high energy end. Similarly, the deviations of DNA-Opt6 from ICRU are also slightly higher than the present model.