Numerical approximation for the radiation shielding properties of borosilicate glasses with ZnO using piecewise cubic Hermite interpolating polynomials and Akima interpolation

This work presents an in-depth analysis of the linear attenuation coefficient (LAC), effective atomic number (Z_eff) and half value layer (HVL) for borosilicate glasses doped with ZnO. Utilizing Akima splines and piecewise cubic Hermite interpolating polynomials (PCHIP), we predicted the LAC, Z_eff and HVL for the investigated glasses in a wide energy range of 0.015–15 MeV. The results showed that the LAC values for the four prepared glasses predicted by Akima splines and PCHIP closely match the theoretical data at all the selected energy levels. This suggested that both Akima splines and PCHIP are a reliable technique for evaluating the LAC of the prepared borosilicate glasses in the energy range of 0.015–15 MeV. The same agreement between the theoretical and predicted data was also reported for the Z_eff and HVL. Also, we examined the accuracy in the Akima splines and PCHIP methods in predicting the radiation shielding properties for the selected glasses at certain energy values emitted by Eu-152. The results demonstrated excellent agreement between Akima splines and PCHIP with the theoretical data, which confirms the usefulness of these two interpolation methods in predicting the radiation shielding parameters in the energy range of 0.0395–1.46 MeV.