Calculation of Macroscopic Cross Section and Mean Free Path

Most materials are composed of several elements, and because most elements are composed of several 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 the macroscopic cross section for each isotope and then sum all the individual macroscopic cross sections. Equation (2-4) can be used to determine the macroscopic cross section for a composite material.

where:
N_n = the number of nuclei per cm³ of the n^th element
σ_n = the microscopic cross section of the n^th element

The following example problems illustrate the calculation of the macroscopic cross section for a single element and for combinations of materials.