Characterization of material using dual-energy gamma-ray tomography: Determination of atomic number and density

Abstract

This study presents a new mathematical model for determining the atomic number and density of materials using dual-energy gamma-ray transmission tomography. The proposed method is based on an algebraic function that relates the atomic number to the attenuation ratio, offering an innovative approach for the precise characterization of materials. The methodology employed involved the theoretical development of the model, followed by tests using data from NIST XCOM and practical experiments with a gamma-ray transmission tomograph using americium-241 (59.5 keV) and cesium-137 (662 keV) sources. Two sets of materials were used: one group of 10 elements for determining the calibration curves and another with 4 elements (graphite, magnesium, aluminum, and iron) for validating the theoretical and experimental calibration curves. Unlike existing methods, which predominantly utilize polynomial or exponential relationships, the proposed model introduces a novel algebraic approach to enhance accuracy and computational efficiency. The performance of the new model was compared with approaches used by other authors. The analyses were conducted for elements with atomic numbers between 6 and 30, covering a significant range of materials of practical and scientific interest. The results demonstrated that the proposed model presented discrepancies of less than 3.5% for the atomic number and a maximum error of 10.04% for the density, with a trend of decreasing errors as the atomic number increased.