Macroscopic Cross Section
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Microscopic cross sections constitute a key parameters of nuclear fuel.
Macroscopic cross section. Find the macroscopic thermal neutron absorption cross section for iron which has a density of 7 86 g cm. Formally the equation above defines the macroscopic neutron cross section for reaction x as the proportionality constant between a neutron flux incident on a thin piece of material and the number of reactions that occur per unit volume in that material. The microscopic cross section represents the effective target area of a single nucleus while the macroscopic cross section represents the effective target area of all of the nuclei contained in certain volume.
The macroscopic cross section defined in section 1 8 4 can be calculated for a compound or a mixture using either the atomic density or the mass density of the constituent nuclides. Here σ which has units of m 2 is the microscopic cross section. The microscopic cross section of the n element n th the following example problems illustrate the calculation of the macroscopic cross section for a single element and for combinations of materials.
It is defined as the probability of incident neutron interacting with the target nucleus per unit length of travel of the incident neutron. While the macroscopic cross section represents the effective target area of all of the nuclei contained in the volume of the material. The distinction between macroscopic and microscopic cross section is that the former is a property of a specific lump of material with its density while the latter is an intrinsic property of a type of nuclei.
The difference between the microscopic cross section and macroscopic cross section is very important and is restated for clarity. The microscopic cross section represents the effective target area of a single target nucleus for an incident particle. The macroscopic cross section denoted by the greek upper case sigma σ and is expressed in units per centimeter travel of the neutron in a medium.
A macroscopic cross section is derived from microscopic cross section and the atomic number density. The units are given in barns or cm2. In terms of atomic density the macroscopic cross section for a compound is calculated from the microscopic cross sections σ i s of the constituents according to eq.
The units are given in cm 1. The larger the neutron cross section the more likely a neutron will react with the nucleus. The microscopic cross section represents the effective target area of a single nucleus while the macroscopic cross section represents the effective target area of all of the nuclei contained in certain volume.
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