A new approach to calculating the ratio of the compton to total, mass attenuation coefficient

Abstract

X-rays and gamma rays are high-energy radiation that ionize atoms of matter as they pass through them. These rays interact with matter in such a way that secondary rays with energy equal to or lower than the incident photon are produced. The buildup factor is used to estimate the intensity of these secondary rays. One of the methods to calculate the buildup factor is the Geometric Progression formula. To use this formula, the equivalent atomic number must be determined. The ratio of the Compton mass attenuation coefficient to the total mass attenuation coefficient (R) is used to calculate the equivalent atomic number for each compound, element, or mixture. In this research, an equation was introduced to calculate the ratio of the Compton mass attenuation coefficient to the total mass attenuation coefficient (R) for X and gamma rays. This equation was the first of its kind and had good accuracy. It was a two-variable function of energy and atomic number that covered the energy range of 0.015–15 MeV and the range of 4–92 for atomic number. The highest SSE and RMSE fitting errors for the energy component for all calculated elements were equal to 0.000921 and 0.0076, respectively, and the same calculation errors for the atomic number component parameters were equal to 9.5561 and 0.7092, respectively. The maximum relative error of the calculated value with the actual value of water as a composition was less than 6%, and the amount of the same error for lead as an element was less than 9%. This equation can be used in other nuclear codes, as the functions used in it are very straightforward. It reduces the speed of calculations and the volume of calculations for calculating the secondary radiation dose.