# Skin Absorbed Dose Coefficients for Human Legs from Beta Radiation as a Function of Height
###### Abstract  
External exposure to skin from beta-emitter radionuclides following severe reactor accidents or nuclear testing can result in beta burning and other health complications. The skin absorbed dose coefficient (SADC) measures the energy deposition into the skin during such accidents. The U.S. Environmental Protection Agency has published several reports to measure the possible energy deposition into the skin in such accidents. However, the most recent SADC published by Federal Guidance Report (FGR) 12 was computed only at one meter above the contaminated surface. Therefore, it was necessary to develop a model to estimate the absorbed dose coefficients for skin at different heights. In this manuscript, Geant4, a Monte Carlo simulator toolkit, was used to estimate the absorbed dose coefficients from electron sources located on the soil surface with energies ranging from 0.1 to 4 MeV. The energy deposited from primary electrons, secondary electrons, and photons in a 50 \(\upmu\)m thick layer of epidermis tissue (Basal Cells Layer) located at a depth of 50 \(\upmu\)m from the skin surface was estimated at several discrete heights of human leg phantom. More than 40% of the total energy deposited comes from secondary electrons and photons in energy sources of 0.1 and 0.2 MeV on average, but for higher energies, this percentage is less than 1%, which indicates primary electrons are the main source of the deposited energy in the skin. Furthermore, the results showed the energy deposited into skin closer to the ground was 50-100% higher than the previously estimated doses for 1 m above the ground. The results from Geant4 showed a great correlation (R\({}^{2}\) = 0.972) with the FGR 12 data at one meter height, and they were aligned with the published values from FGR 12, which validated the simulation results. Therefore, the calculated dose coefficients for different energy sources and different heights could be used in radiation protection measurements. skin absorbed dose coefficient; beta emission; radiation protection; Geant4 2024  
Reactor accidents or nuclear explosions can lead to fission products being deposited into the environment, contaminating water resources, air, and soil. During nuclear accidents, different particles such as beta particles, alpha particles, neutrons, and photons are emitted [7; 8] from fission products. Beta particles are electrons and positrons emitted from the nuclei of unstable atoms, and they have the same mass as electrons [9]. Beta particles can have either a negative or positive charge; a negatively charged beta particle is identical to an electron, while a positively charged one is identical to a positron [10]. Due to their small mass, high-energy beta particles can reach the speed of light [11]. They also lose their energy very fast when they interact with matter; consequently, their range in air or other materials is very limited. The damage that beta particles can cause to materials is less than that of other particles for the same deposited energy [12]. Beta with the negative charge \"\(e^{-}\)\" decays when a neutron \"\(n\)\" becomes a proton \"\(p\)\" and an antineutrino \"\(\overline{v}\)\" are emitted [13]:  
\[n\ \rightarrow\ p+\ e^{-}+\overline{v} \tag{1}\]  
A positron \"\(e^{+}\)\" (Beta particle with a positive charge) decays when a proton becomes a neutron and a neutrino \"\(v\)\" are emitted as [14]:  
\[p\ \rightarrow\ n+\ e^{+}+v \tag{2}\]  
Beta particles are one of the main radiation products at nuclear accident sites that can cause severe skin burns as they can penetrate the outer layers of the skin [15; 16; 17; 18; 19]. Therefore, estimating the absorbed dose to human skin layers from beta emissions at contaminated incident sites is important. Beta decay from fission products has a spectrum energy ranging from a few keV to about 5 MeV [20; 21]. [PERSON] et al. studied the beta decay spectrum for about a hundred different radionuclides [22]. The energy spectrum range for the isotopes started from 0 to 4 MeV, and very few exceeded 4 MeV.