# Simulation and Evaluation of the Radiation Dose Deposited in Human Tissues by Atmospheric Neutrons
## 3 Results and Discussion  
When calculating the RD that neutrons deposit in the different sample tissues, under the conditions mentioned in the previous section, we obtained the statistical error less than 1% for each calculated value. Since statistical errors are relatively small, we decided not to point them out in Figure 3 that we present in this section. In Figure 3, we show the RD that neutrons deposit in the samples as a funtion of their kinetic energy. In this figure, we can see three sections with different behavior of the RD deposited in the samples as a function of the energy of the neutrons; first, for energies of 1  
Figure 2: Atmospheric neutron spectra for various latitudes at geographical points with an altitude of 10 km and a longitude of 0\({}^{\circ}\). See text for more details. to 20 MeV the RD curves show an increase with the energy of the neutrons; second, for energies of 20 to 500 MeV the RD curves are approximately flat; finally, for greater energies at 500 MeV the RD curves show an increase with the energy of the neutrons. In Figure 3, we can also observe that, neutrons with energy less than 200 MeV deposited a less RD in the bone sample compared with the RD deposited in the other samples, whereas that, the RD deposited in the adipose sample is greater than the RD deposited in blood and brain samples; this is due to the chemical composition of the tissues, for adipose tissue the dominant element is carbon, for blood and brain tissues is oxygen and for bone tissue are oxygen together with calcium. Neutrons with energy equal or greater than 200 MeV deposited a higher RD in the bone sample compared with the RD deposited in the other samples, this occurs because the cross section of the neutron varies with the kinetic energy of this particle. Considering the RD deposited by the neutrons in the bone tissue sample as a reference, in the range of energies from 1 to 100 MeV, the RD deposited in the blood, adipose and brain tissue samples are 167.9%, 182.8% and 172.3% respectively; while, for the range of energies between 200 and 1000 MeV, the RD deposited in the blood, adipose and brain tissue samples are 81.0%, 80.8% and 80.5% respectively. The neutron fluxes as a function of the altitude and the geographical latitude were calculated under the conditions mentioned in the previous section. In Figure 4, we show the RD that neutron with energies between 1 and 1000 MeV deposited in the tissue samples for an altitude between 0 and 10 km above sea level. To avoid overlapping of the curves, we have multiplied them by a factor shown in their respective labels. In Figure 4, we can see that the RD deposited in the tissue samples is minimal at sea level and increases with height, the reason for this is that the neutron flux increases with increasing height. All curves have the same behavior. From the data obtained from the simulation and considering as reference the RD deposited by neutrons at 0 km above sea level, for an altitude of 4 km, corresponding approximately to an altitude of high mountain, the RD is increased \(\sim\)19 times, while, for an altitude of 10 km, corresponding to an altitude of commercial flights, the RD is increased \(\sim\)156 times. Figure 3: Radiation dose deposited by \(5\times 10^{5}\) neutrons to each energy in the tissue samples. This result was obtained by a numerical simulation. In Figure 5, we show the RD that neutron with energies between 1 and 1000 MeV deposited in the tissue samples as a function of the latitude for an altitude of 10 km above sea level and a longitude of 0\({}^{\circ}\). To avoid overlapping of the curves, we have multiplied them by a factor shown in their respective labels. We can see that the RD deposited in the tissue samples is lower in equatorial zones (\(\sim\)0\({}^{\circ}\)); the above is due to the fact that in these zones the rigidity cutoff is maximum, containing lower flux of cosmic rays and consequences a lower production of atmospheric neutrons.