An approximation of mass attenuation coefficients of Li₂O–Fe₂O₃–In₂O₃–Bi₂O₃-P₂O₅ glasses using cubic spline and Akima interpolation

In order to expand the range of techniques used to explore the efficiency of gamma ray shielding materials, the feasibility of cubic spline and Akima interpolation methods in predicting of the mass attenuation coefficients (MACs) values was examined A series of Li₂O–Fe₂O₃–In₂O₃–Bi₂O₃–P₂O₅ glasses were proposed, and their mass attenuation coefficients were calculated using the two methods and compared with that estimated using the standard Phy-X software to check their accuracy. The tested energies were divided into a set of 42 discrete energy ranges, where at each range four coefficients were determined for each glass using MATLAB. The CS and Akima interpolation values were then graphed as a function of energy alongside the theoretical MAC values, demonstrating a strong agreement between the two methods and the Phy-X values. For example, the Phy-X value for the S1 glass at 0.2600 MeV is equal to 0.1208 cm²/g, while the CS and Akima interpolation values are 0.1208 and 0.1217 cm²/g, respectively. Because of the excellent predictive abilities of these methods, both the CS and Akima interpolation mathematical models are useful tools to anticipate MAC values at any energy within the range of the given data set.