Unscattered Flux from Spherical and Cylindrical Sources with Shell-Shaped Shields

Abstract

The effect of shell-shaped shield surrounding a spherical or cylindrical source is studied. The shapes of different shields with a common attenuation parameter μt is classified into six types according to the positions of the inner and outer surfaces with respect to the source and the detector. The exact equations and their approximate formulas for unscattered fluxes from sources with shell-shaped shields are derived. The difference between the results from the approximate and the exact calculations is less than ±2% for dense and/or large sources (μ₈R₀≳4), and ±20% for small and/or thin sources (μR_o≳4). Functions expressing the effect of shield shape are also derived. This effect is very large, and sometimes reaches a factor of from 2 to 10. The results of calculation for spherical sources are compared with those by Ascoli, and it is found that his approximate method has a large error for large sources and/or dense shields (μR₀≳4). The results of calculation for cylindrical sources agree well with those by Taylor and Obenshain, and also with Osano v 8 experiments.