Looking at Figure 5, the relationship between the attenuation (loss) of photons as a function of distance from the rack is a purely exponential decay. Plotted on a log scale, this is shown as a straight line with negative slope. This makes perfect sense, as the further into the geometry the photons go, the more opportunities they have to interact with the atoms that make up the system. The more potential interactions the photon has, the more interactions occur. As a result, the number of photons rapidly diminishes as they move through the geometry. Note also that there is a peak just in front of the source at around 3 cm from the rack. This peak is due to the fact that at the center of the rack, the only contributions to the flux are from the interior sources. The photon contributions from the outer sources are blocked, or shielded from this location by the superposition of interior structures. In other words, in the center of the rack, the outer sources do not fully impact the flux; however when you move slightly away from this position, there are no structures to shield photons, and therefore a higher flux is seen. There are two basic modes for the attenuation of photons seen in Figure 5, geometrical and interaction based. Here, because the material (water) is so dense, the primary mode of attenuation is particle interactions. The average path that a photon can travel before interacting with another atom is very small because the atoms are very close together. So, the photon deposits some of its energy into the material every time it has an interaction and thus quickly deposits all of its energy. Therefore few photons survive past 80 cm of water. Though interaction based attenuation is the dominant factor, geometrical attenuation also is present. Notice that the photon flux is spread out like a normal wave function. This is not at all surprising as photons regularly behave as waves. As the wave spreads out, the flux of the photons must also lessen as they move to fill the available space. Because there is more space to fill as this plane wave grows, the amount of photons present at these locations must necessarily decrease. Shifting focus to the second model, the gamma flux profile through the Gamma Irradia26 UMLJUR
tion Facility as a function of distance can be seen below. As can be seen from Figure 7, the flux profile again attenuates in an exponential-like fashion with respect to distance from the rack. On the surface, these figures are very similar to the flux profiles for the rack in water, however there are subtle differences. First, the rate at which the photon flux decays is much faster in the water geometry. For example, in Figure 5 the flux decays by three orders of magnitude around 80 cm while in Figure 7, the flux profile never fully reaches a comparable level even after 250 cm. This is because the interaction attenuation is much stronger in the water geometry. The water is much denser than air and therefore the gamma photons are forced to have more interactions over a certain distance. Since the photon losses some of its energy in every interaction, total energy deposition occurs much quicker in water than in air. The differences between these two models are more apparent as the distance from the rack increases. This is partly because photons do interact with water for the first 2 cm of their journey before they cross the aluminum wall and enter the facility. Note from Figure 7 that the attenuation in the irradiation facilities is not purely exponential. When plotted on a log scale, a purely exponential function will appear as a straight line like in the water model. However, this is not what is seen in the Gamma Irradiation Facility geometry. This observation is due to the fact that the geometry of the system dominates the photon attenuation. The photon interaction with air is sparse because air has a low density. A low density means less objects for the photons to interact with, and thus less interactions. Also, in the irradiation facilities model, the geometry “opens up� at several different locations, which allows the photons to spread out. The two primary locations that this spreading out occurs is when the aluminum wall ends and the photons enter the air, and when the window structure ends and the photons enter the free space of the entire room. These effects can clearly be seen by looking at the logarithmic plot of flux as a function of distance. For a very small distance from the source, the attenuation is almost purely expo-