A probabilistic derivation of gamma-ray attenuation and application: Bayesian mass estimation with a low count spectrum

This paper presents an intuitive derivation of the source and absorber factors in a slab geometry formulation of γ-ray emissions incident on a detector. Using the attenuation equations, an application to mass estimation from a passively observed, low count spectrum is developed for sources with γ-ray emissions. Propagation of error provides a confidence interval on the mass estimate. The developed methods are applied to experimental spectra from a known mass of plutonium 239 oxide. The proposed estimation method has potential in national security applications where the geometry of attenuation materials is unknown and there are time constraints on the acquisition of a spectrum. In these application settings, the first-order mass estimate developed in this paper is sufficiently accurate.