'()DOE-HDBK-1019/1-93Reactor Theory (Neutron Characteristics)NUCLEAR CROSS SECTIONS AND NEUTRON FLUXRev. 0Page 11NP-02CalculationofMacroscopicCrossSectionandMeanFreePathMost materials are composed of several elements, and because most elements are composed ofseveral isotopes, most materials involve many cross sections, one for each isotope involved.Therefore, to include all the isotopes within a given material, it is necessary to determine themacroscopic cross section for each isotope and then sum all the individual macroscopic crosssections. Equation (2-4) can be used to determine the macroscopic cross section for a compositematerial. *= N ) + N ) + N ) + ....... N )(2-4)1 1 2 2 3 3 n nwhere:N= the number of nuclei per cm of the n element n3 th)= the microscopic cross section of the n elementnthThe following example problems illustrate the calculation of the macroscopic cross section fora single element and for combinations of materials.Example 1:Find the macroscopic thermal neutron absorption cross section for iron, which has adensity of 7.86 g/cm . The microscopic cross section for absorption of iron is 2.56 barns3and the gram atomic weight is 55.847 g.Solution:Step 1:Using Equation (2-1), calculate the atom density of iron.Step 2:Use this atom density in Equation (2-2) to calculate the macroscopiccross section.