Diffusion of High Energy Gamma-Rays through Matter. I. Fundamental Equations

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Abstract
The fundamental processes, photoelectric absorption, Compton scattering, and pair production, leading to the modification of the energy spectrum and angular distribution of gamma-rays diffusing through matter are discussed in relation to the problem of penetration of gamma-rays through matter. The transport equation describing the diffusion is derived in the approximation in which radiation from the secondary electrons produced by the photoelectric effect and pair production is neglected. By limiting one's interest to gamma-rays of energy greater than a few Mev, further approximations may be made which reduce the transport equation to a much more simple form. An elementary proof is given for the following theorem: If monoenergetic gamma-rays are incident normally on a slab of material, then after the gamma-rays have undergone many Compton scatterings, the gamma-rays of a given energy are distributed Gaussian-wise in angle about their original direction with the breadth of the distribution being simply related to the energy and increasing with decreasing energy.