Mathematical formula to calculate the attenuation coefficients for any complex sample: experimental study

Abstract

This work introduces a mathematical formula to calculate the attenuation coefficient of a cylindrical sample placed on the top of a well-shaped gamma-ray detector. The formula depends on calculations of the average path length of the photon through a sample and the effective solid angle. The obtained results using the introduced formula are compared with the NIST XCOM database and compared with the experimental work using two different-sized detectors and sources located in two different positions. A remarkable agreement between both was observed, which proves the validity of this formula.