# Skin Absorbed Dose Coefficients for Human Legs from Beta Radiation as a Function of Height
## 3 Results and Discussion  
The skin absorbed dose coefficient (SADC) for different energy sources is calculated using Geant4 simulations for different heights of the leg; the total SADC and the SADC from primary electrons are compared to the SADC obtained from secondary electrons and photons. For each energy source, 2 billion beta particles were generated randomly from the cylindrical electron source at the top of the soil. The number of particles entering each detector as well as the deposited energy in keV were calculated. The mass for the basal layer was calculated using its volume and density. The absorbed dose delivered to the basal layer was calculated by dividing the deposited energy by its mass, and then the absorbed dose per particle was calculated for each cell by dividing the absorbed dose by the total number of events generated. Finally, the SADC for each basal layer was calculated by multiplying the absorbed dose per particle by the source area, as follows:  
\[SADC=\frac{E\times A}{M\times p} \tag{8}\]  
where SADC is in \(\upmu\mathrm{G_{y}}\cdot\mathrm{m^{2}}\) per particle, E is the deposited energy in keV, M is the mass of the basal layer in kg, A is the area of the source in \(\mathrm{m^{2}}\), and p is the total number of generated particles. Similar calculations are conducted to calculate the SADC from secondary electrons and generated photons during the simulations. The absorbed dose coefficient comparison between the total absorbed dose and the dose from primary electrons (electron only) for different heights of the leg is depicted for energy sources 0.1 MeV and 0.2 MeV in Figures 4 and 5, respectively. For the sources with low energies (0.1 and 0.2 MeV), primary electrons deliver a very low absorbed dose to basal cells, especially for the cells with heights greater than the CSDA range. The simulation results in Geant4 showed that for higher energies, more than 99% of the deposited energy in leg cells comes from the tracked primary electrons originating directly from the ground beta source. The absorbed dose coefficient for energy sources of 0.4, 0.8, and 1.0 MeV is shown in Figure 6. The total skin absorbed dose for energy sources of 1.5, 2.0, and 2.5 MeV, as well as the total skin absorbed dose for 3.0 and 4.0 MeV energy sources, are displayed in Figures 7 and 8, respectively. Figure 4: Skin absorbed dose coefficient for 0.1 MeV source for electrons only and total deposited energy. Figure 5: Skin absorbed dose coefficient for 0.2 MeV source for electrons only and total deposited energy. Figure 6: Total skin absorbed dose coefficient for 0.4, 0.8, and 1.0 MeV. Figure 7: Total skin absorbed dose coefficient for 1.5, 2.0, and 2.5 MeV. For sources with lower energies (0.1 and 0.2 MeV), the share of generated photons and electrons in the deposited energy in the human leg cells was much higher. The share of secondary electrons and generated photons in the deposited energy in cells with a higher height than 10 cm (after the third cell) for the 0.1 MeV source jumped from 1% to more than 40% of the total deposited energy. The percentage of the absorbed dose from photons in the total deposited energy in the phantom leg is depicted in Figure 9. For the electron source with 0.1 MeV, when the height of cells exceeds the CDSA range (13.5 cm), a sharp increase in the percentage share of photons happens. Expectedly, the increase in the percentage share of photons for 0.2 MeV occurs for higher cells, as the CDSA range for 0.2 MeV is about 42 cm. For the source with 0.4 MeV, only the very top cell of the phantom leg has considerable deposited energy from photons. For the other energy sources, photons and secondary electrons make up less than 1% of the total deposited energy into the leg. Since it is expected from the physics of the problem to see this pattern in the deposited energies for different energy sources, this graph validates the simulation results. Different factors could affect the results from the Geant4 simulations for the human leg.