## 2 Materials and Methods
### MCNP Setting for the Simulations of Our Study  
Estimation of the absorbed dose to tissues of the human body, from radiations emitted by an arbitrary distribution of a radionuclide in an environmental medium is an extremely difficult computational task. By using the MCNP code, we create the geometry of the experimental setup. In this case, we base our simulations on a \"human phantom\" (filled with water as content), which appears as a cylinder with a radius of 25 cm and 180 cm in height, simulating an average man standing on the soil at the air-ground interface. This phantom is separated into layers of 10 \(\upmu\)m thickness, which represents the typical average size of a eukaryotic mammalian cell (Figure 1). Figure 1: MC geometry model of the MCNP6.1 simulation including the source, the phantom and all the patterns used in it. The whole setting is as follows: the human phantom (depicted as a blue thin cylinder of 1.80 m height and 25 cm radius) stands in the middle of the outer azure cylinder (radius 20 m) which is filled with air (surrounding environment). The grey base cylinder (radius 20 m) represents the source volume on which the “human” stands (i.e., the surrounding ground, composed of soil and contaminated with the radionuclide \({}^{137}\)Cs in different surface activity values). There is no proportionality in the depicted dimensions of the patterns for the sake of simplicity. Additionally, an isotropically distributed cylindrical source of \({}^{137}\)Cs has been placed in the ground, at a depth of 20 cm; the latter value represents a mean typical depth of radiocasium deposition in soil after its release as a consequence of a nuclear accident [48]. We have chosen to use this specific value for the deposition depth of \({}^{137}\)Cs in all our measurements, since many fundamental studies about the vertical distribution of this key artificial radionuclide in the environment show its biggest concentrations in the topsoil layers, especially above the depth of 20 cm [5; 49; 50]. The content of this radionuclide in soil is influenced by vertical migration due to the physical processes of diffusion, convection transfer with the soil moisture, and migration through the roots of plants. Generally, the concentration of radiocasium is decreased exponentially with depth, depending on the landscape and mainly the soil type; the latter includes factors such as the mineral and physical composition of the soil, its organic composition, cation exchange capacity, acidity, and the presence of certain kinds of vegetation (e.g., coniferous trees and mosses which play the role of a filter, engulfing radionuclides for long periods after the initial fallout) [51; 52; 53; 54; 55]. In our study, we have considered an isotropic cylindrical source (the base cylinder in Figure 1) and, therefore, in our simulations we have planned its surface area (base of the cylinder) to be 1256 m\({}^{2}\) (radius 20 m). Of course, a larger source area would result in a higher effective dose to our phantom, but based on the results of a similar study by [PERSON] et al., 2010 [56] where the effective dose proves to increase \(<\)2% when the source area increases by 78%, we have assumed in all our simulations that a source area with the aforementioned value is a reasonable one, representable of a contaminated area beneath the ground. In our study, the material which is mixed with the source of gamma rays (\({}^{137}\)Cs) includes all those elements contained in soil in the respective proportions (mass percentage) (i.e., Si: 27.1183%, Fe: 5.6283%, Mg: 1.3303%, K: 1.4327%, Ca: 5.1167%, O: 51.3713%, Na: 0.614%, Al: 6.8563%, Ti: 0.4605% and Mn: 0.0716%), considering a typical value of dry density \(\sim\)1.52 g/cm\({}^{3}\)[57]. The entire assembly is surrounded by air (i.e., the external cylinder in which the human phantom stands).