Single Scattering Streaming of Gamma-Rays through Cylindrical Ducts

Abstract

An exact equation, for use in the calculation of the γ-ray streaming after single scatterings in a cylindrical duct, and its approximate formula, are presented. The dose of single scatterings at the exit of a cylindrical duct from a disk source at the entrance can be approximated by
D={4π/(n+1)}S_ak₁E₀Q(L/R₀)^-2 for s0 ?? L/R₀ ?? s1
={4π/(n+1)}S_ak₂E₀Q(L/R₀)^-3 for s1 <L/R₀ ?? 60,
where D = dose at the exit of the duct, S_a = source strength, n = a parameter of the angular distribution of the source, E₀ = energy of the source photons, Q = conversion factor, R₀ = duct radius and L= duct length.
The coefficients k₁ and k₂, as well as the constants s₀ and s₁ vary with source energy and wall materials. The values for lead, iron, concrete, tin, magnetite concrete, graphite and water are given in graphical representation for an energy range from 0.5 to 10 MeV.
A study is made of the distribution of the arrival probabilities of photons, corresponding to the positions of scattering points for the photons from the source to the duct exit. It was found that the effective scatterings contributing to the flux at the exit occur mainly in the shallow part of the duct wall, near its surface.