When calculating the thickness of a radiation shield, what extra factor must be used to account for gamma rays that bounce off atoms inside the shield and still escape?

The extra factor that must be used to account for gamma rays that bounce off atoms inside the shield and still escape is called the build-up factor. When gamma rays penetrate a shield, they can interact with the electrons and nuclei within the shielding material. A predominant interaction for gamma rays in the energy range relevant to shielding is Compton scattering, where a gamma ray photon collides with an electron, transferring some of its energy to the electron and changing its direction. Although some gamma rays are absorbed or scattered completely away, many undergo one or more scattering events within the shield and still exit the material, albeit with reduced energy and a altered trajectory. These internally scattered gamma rays contribute to the total radiation dose outside the shield. Simple exponential attenuation calculations, which are fundamental for determining shield thickness, typically only account for the primary or unscattered radiation that passes directly through the material without interaction. These calculations do not inherently consider the additional dose contribution from the scattered photons. The build-up factor explicitly corrects this by serving as a multiplier to the dose calculated from primary radiation alone. It is defined as the ratio of the total radiation dose or flux (comprising both the unscattered primary radiation and the secondary scattered radiation) to the dose or flux contributed solely by the unscattered primary radiation. The magnitude of the build-up factor is influenced by several key parameters, including the atomic number and density of the shielding material, the thickness of the shield (often expressed in terms of mean free paths or relaxation lengths), and the energy of the incident gamma rays. Incorporating the build-up factor ensures that the calculated shield thickness effectively accounts for all radiation reaching the protected area, including the scattered component.