# Extension of the Discrete Electron Transport Capabilities of the Geant4-DNA Toolkit to MeV Energies
## 2 Materials and Methods  
### Basic Features of the Present Model  
In both DNA-Opt2 (default constructor) [15] and DNA-Opt4 (recommended low-energy constructor) [43; 44], the inelastic model used to calculate the excitation and ionization cross sections is based on a semi-empirical dielectric response function determined by an optical-data model [8]. This approach is considered the state-of-the-art for practical calculations of inelastic electron-scattering in condensed medium (e.g., liquids, solids) [1; 9; 11; 46; 47; 48; 49], as it is based on the well-established theoretical framework of the first Born approximation while offering a reasonable balance between computational simplicity and robustness. Although ab initio approaches offer far more detail and are theoretically rigorous [51; 52], they are still not as attractive as the semi-empirical optical-data models, at least for those materials (like liquid water) where experimental optical data are available, due to their theoretical complexity and higher computational cost. Optical-data models commonly employ either a Drude-type or a Lindhard-type or a Mermin-type representation of the dielectric function [1; 46; 47; 48; 49]. The Drude-type representation, which is mathematically (and computationally) simpler, is used in both DNA-Opt2 and DNA-Opt4, as well as by other popular MCTS codes for liquid water, like NOREC [53], PARTRAC [54], and KURBUC [55]. The theoretical framework adopted in the present work for the calculation of electron inelastic cross sections is the Relativistic Plane Wave Born Approximation (RPWBA) where the probability of ionization and excitation of the medium is essentially described by the energy loss function (ELF) which is defined by the imaginary part of the reciprocal dielectric function (see below). The present inelastic model, hereafter denoted as \"DNA-Opt4X\", includes all the latest modifications to the ELF (presented in [43; 44; 50]) that reduced the sum-rule errors to less than 1.5% (from 6.5% in DNA-Opt2). In addition, both the low- and high-energy corrections are implemented as described in [50]. However, to efficiently extend the model above 1 MeV, additional corrections and modifications have been implemented as will be described in the next sections. Since the various corrections involve additional cross section calculations (which are often far more time-consuming per data point than the uncorrected calculations), we restrict the application of each correction to specific energy regimes where a sizeable impact is expected (see Figure 1). The optimum transition energy (from one regime to the next) may depend on the application. As a first approximation, we here adopt a more general approach (also used in [50]) where the transition energy is based on the impact of the correction to a fundamental and well-understood radiation dosimetry quantity, namely, the electronic stopping power. Therefore, corrections are applied only within the energy range in which their individual effect on the electronic stopping power is larger than 1%. Based on this criterion, and in order to make the model implementation more transparent to future modifications, we distinguish between four energy regimes as depicted in Figure 1.  
In the existing dielectric models of Geant4-DNA, the inelastic cross sections are calculated off-line and implemented into the code via look-up tables, so the complexity of the inelastic physics model does not have any impact on the simulation running times (apart from the rather small influence of the different energy binning between different models). Thus, the implementation (or not) of the various corrections (see Figure 1) does not (practically) influence simulation running times. However, simulations by DNA-Opt4X are faster (depending on the specific application) than the current default constructor (DNA-Opt2) due to the different elastic models used.