Development of Mathematical Model to Predict Mass Attenuation Coefficient of Silicate Glasses By using Polynomial Curve Fitting

In this study, the 13th-order polynomial curve fitting was successfully derived from the coefficients obtained through curve fitting. This polynomial serves as a powerful mathematical model that accurately captures the intricate relationship between the mass attenuation coefficients (MAC) and energy for our glass samples. The significance of this polynomial representation lies in its versatility and predictive capability. The difference between the theoretical and predicted MAC for the S1 sample at 0.200 MeV is 0.0015 cm 2 /g, while it is equal to 0.0001 cm 2 /g for the S5 sample at 0.800 MeV. Moreover, at 1.275 MeV, the theoretical MAC value for S1 is equal to 0.0561 cm 2 /g, while the predicted value is equal to 0.0591 cm 2 /g. The MAC of the S4 sample at 0.511 MeV is equal to 0.0861 and 0.0862 cm 2 /g for the theoretical and predicted values respectively. The extremely small difference between the theoretical and predicted values demonstrates the potential for this model. Additionally, with this polynomial equation at our disposal, we have the means to anticipate MAC values at any energy within the studied range, even for energies not included in the original dataset. This mathematical model facilitates our ability to design and optimize radiation shielding materials, plan experiments, and address questions related to the behavior of the selected glasses under varying ionizing radiation conditions. In our pursuit to comprehensively explore the MAC-energy relationship and validate the obtained polynomial models, we meticulously selected a set of energy values for which MAC predictions are both desired and essential.