# Extension of the Discrete Electron Transport Capabilities of the Geant4-DNA Toolkit to MeV Energies
## 1 Introduction
Owing to the special role of electrons (both as primary and secondary particles) in MCTS simulations, the Geant4-DNA toolkit [8; 14; 15; 16; 17], includes a variety of different physics models to describe each type of interaction (i.e., ionization, electronic excitation, and elastic scattering). Furthermore, there are some ready-to-use sets of physics models for Geant4-DNA users, known as \"constructors\", that gather the most significant physical processes [8; 17]. Although important efforts are currently invested to describe electron interactions in DNA-like materials using measured or calculated cross sections for individual DNA bases (in the gas phase) [41; 42], liquid water remains the most generic transport media in radiobiological applications, since cells are mostly composed of water (70-80% by weight), which is also the source of reactive free-radicals. The different \"constructors\" (and physics models) for liquid water medium currently available in Geant4-DNA have been described in detail in previous works [43; 44; 45]. Historically, an important challenge to the development of MCTS codes is the calculation of low-energy inelastic cross sections for all the ionization shells and electronic excitation levels of the irradiated medium down to threshold energies (\(\sim\)10 eV). Nowadays,the most established MCTS codes for liquid water calculate inelastic cross sections via a semi-empirical model of the dielectric response function of the medium [1; 9; 11; 46; 47; 48; 49]. The attractive feature of this approach is that condensed-phase effects, which are crucial for modeling radiation interactions in biological matter at the nanoscale, are in-built into the methodology. Currently, the most accurate low-energy electron inelastic model in Geant4-DNA is implemented into the DNA-Opt4 constructor [43; 44]. However, its upper energy limit of 10 keV, prohibits using it in many practical (e.g., clinical) applications. So, in order to cover medium-high energy applications, Geant4-DNA users need to combine DNA-Opt4 (<10 keV) with the default constructor DNA-Opt2 (>10 keV) [17]. Therefore, the extension of the inelastic model of DNA-Opt4 to higher electron energies (its elastic model is already applicable to relativistic energies) has become a \"physics-activity\" priority for the Geant4-DNA collaboration. To that end, a preliminary relativistic extension of DNA-Opt4 was recently presented (referred to as DNA-Opt4 Rel in [50]), focusing mostly on refinements of the dielectric response function and the presentation of the needed relativistic modifications to reach Geant4-DNA's current upper electron limit of 1 MeV. The aim of this work is to document a complete relativistic version of the inelastic model of DNA-Opt4 (hereafter termed DNA-Opt4X) which improves and extends Geant4-DNA capabilities up to 10 MeV. The full set of ionization and excitation cross sections implemented into this new constructor (DNA-Opt4X) are presented, and benchmark simulations of the electronic stopping power and range of electrons in liquid water are performed and assessed against the available ICRU data. An intercomparison between the new (DNA-Opt4X) and existing inelastic models (DNA-Opt2, DNA-Opt6) of Geant4-DNA is also provided. Unless otherwise stated, energy, momentum, and mass are expressed in units of eV, eV/c, and eV/c\({}^{2}\), respectively, where 1 eV = 1.602 \(\times\) 10\({}^{-19}\) joule and c\({}^{2}\) = 931.46 MeV per atomic mass unit (amu).