Analytical and Experimental Study of X-ray Absorption Coefficients of Material by Abel's Inversion

TL;DR

This paper combines theoretical modeling and experimental measurements to accurately determine X-ray absorption coefficients of materials using Abel's inversion, addressing discrepancies through advanced numerical methods and experimental optimizations.

Contribution

It introduces a new numerical solution to Abel's integral equation and applies it to gamma-ray absorption measurements, improving accuracy in quantitative radiography.

Findings

Enhanced numerical code improves absorption coefficient calculations.

Discrepancies explained by filtering, reflections, and impurities.

Optimal experimental conditions identified for gamma-ray diagnostics.

Abstract

The hard x-ray gamma-ray absorption by cylindrically symmetric U-238 test objects is studied by means of gamma-ray transmission measurements. To make a precise comparison between the theoretically modelled values and the absorption coefficients calculated from the experimental data, we have developed a highly accurate numerical code based on a new solution of Abel's integral equation. It is shown that progressive filtering, surface reflections by Compton scattering, and the enhanced backscattering due to impurities can explain much of the observed discrepancy. We also discuss optimal experimental conditions with regard to the feasibility of quantitative radiography for gamma-ray diagnostics.