Calculate the average macroscopic total cross-section of Be, C, Fe, and Pb for neutrons from a Cf-252 source based on neutron energy group model

Abstract

This study presents an analytical calculation method based on neutron energy group models for calculating the spectrum-averaged macroscopic total cross-sections of Be, C, Fe, and Pb for the Cf-252 fission neutron spectrum using neutron energy group models. Calculations were performed with 11-group and 22-group structures based on microscopic cross-section data from a nuclear data library. The calculated macroscopic total cross-sections obtained with the 11-group model were 0.3170, 0.1689, 0.2542, and 0.2107 cm⁻¹ for Be, C, Fe, and Pb, respectively, while the corresponding values from the 22-group model were 0.3041, 0.1684, 0.2507, and 0.1939 cm⁻¹. Comparison with published MCNP results showed deviations ranging from -2.2% to 2.4% for the 11-group model and from -6.2% to -1.2% for the 22-group model. In contrast, calculations based on a single neutron energy equal to the average energy of the Cf-252 spectrum produced significantly larger errors. The results demonstrate that multi-group treatment of the neutron spectrum is essential for reliable cross-section calculations and that the 11-group model provides a practical combination of accuracy and computational simplicity for educational and shielding applications.