Theory and numerical modeling of x‐ray fluorescence from multi‐layer spheres

A mathematical model has been developed for the quantitative x‐ray fluorescence spectrometry of small spherical samples, e.g. targets containing diagnostic materials for inertial confinement fusion experiments. The model corrects for matrix effects in a multi‐layer spherical geometry much as existing programs now do for thin films or bulk samples. Attenuation effects have been found to be greater in a shell geometry than in a comparable thin‐film geometry because multiple passes through the shell are possible and because many paths in or out are nearly tangential to the shell. In both cases the path is longer and attenuation is greater. The model for primary fluorescence from uniform shells has also been extended to approximate the fluorescence from non‐uniform shells. This allows one to predict how experimental results would vary with sample mounting if excess material were oriented toward or away from the x‐ray beam or the detector or away from both. Finally, a simplified model for estimating the magnitude of secondary fluorescence effects is presented.