# Extension of the Discrete Electron Transport Capabilities of the Geant4-DNA Toolkit to MeV Energies
## 4 Conclusions  
The recommended Geant4-DNA inelastic constructor (DNA-Opt4) for low-energy track-structure simulations has been improved and extended from 10 keV to 10 MeV using the relativistic plane wave Born approximation and other theoretical considerations. Based on this development, a full set of differential and total ionization and electronic excitation cross sections, spanning the energy range from 10 eV to 10 MeV, has been calculated and implemented into Geant4-DNA via a new constructor called DNA-Opt4X. Benchmark simulations of the electronic stopping power and range (or average pathlength) by DNA-Opt4X are carried out and shown to be in almost excellent agreement (at the few % level) with the latest ICRU recommendations. The present results offer significant improvement (by a factor of \(\sim\)2) over the default Geant4-DNA constructor (DNA-Opt2) and an order-of-magnitude higher electron transport limit. This development will allow Geant4-DNA users to perform for the first time electron track-structure simulations, including nano- and micro-dosimetry calculations, up to 10 MeV, thus, covering a wider range of radiotherapeutic applications, including FLASH EBRT, as well as space applications involving MeV electron which are not currently reachable by the existing Geant4-DNA constructors.  
Conceptualization, D.E., I.K., S.I. and V.I.; methodology, I.K. and D.E.; software, I.K., S.I. and H.N.T.; validation, I.K. and H.N.T.; formal analysis, I.K. and D.E.; investigation,  
Figure 9: (**Top** panel) range (or average pathlength) of electrons in liquid water over the energy range from 20 eV up to 10 MeV simulated by different Geant4-DNA constructors, namely, DNA-Opt2 (default), DNA-Opt4X (present/new), and DNA-Opt6, and compared against the range values of ICRU Report 90 [59]; (**Bottom** panel) Percentage difference in the various Geant4-DNA constructors from ICRU [59].  
I.K. and D.E.; data curation, I.K. and D.E.; writing--original draft preparation, I.K.; writing--review and editing, D.E., I.K., S.I., V.I., S.G., L.D. and H.N.T.; supervision, D.E., I.K. and S.I.; project administration, I.K., D.E., S.I., G.S. and P.N.; funding acquisition, D.E., I.K., S.I., L.D., G.S. and P.N. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the European Space Agency (ESA) under contract \"BioRad III\" No. 4000132935/21/NL/CRS (2021-2023) as well as the project FNS Synergia grant MAGIC-FNS CRS II5_186369.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.  
List of Abbreviations  
\begin{tabular}{l l} BEAX & Binary Encounter Approximation with Exchange \\ DCS & Differential Cross Section \\ EBRT & Electron Beam Radiation Therapy \\ ELF & Energy Loss Function \\ ICRU & International Commission on Radiation Units and Measurements \\ Geant & Geometry And Tracking \\ MCTS & Monte Carlo Trak Structure \\ PWBA & Plane Wave Born Approximation \\ RPWBA & Relativistic Plane Wave Born Approximation \\ RT & Radiation Therapy \\ SP & Stopping Power \\ TCS & Total Cross Section \\ CSDA & Continuous Slowing Down Approximation \\ \end{tabular}  
List of Nomenclature  
\begin{tabular}{l l l}
**symbol** & **nomenclature** & **dimensional units** \\ \(T\) & kinetic energy & energy \\ \(E\) & energy transfer & energy \\ \(q\) & momentum transfer & (mass)-(length)-(time)\({}^{-1}\) \\ \(\varepsilon\) & dielectric function & – \\ \(\sigma\) & cross section & (length)\({}^{2}\) \\ \(\alpha_{0}\) & Bohr radius & length \\ \(N\) & density of water molecules & (length)\({}^{-3}\) \\ \(B\) & binding energy & energy \\ \(U\) & average kinetic energy in shell & energy \\ \(m\) & electron rest mass & mass \\ \(\beta\) & particle velocity over speed of light & – \\ \(c\) & speed of light & (length)-(time)\({}^{-1}\) \\ \(Q\) & recoil energy & energy \\ \(R\) & range & length \\ \end{tabular}