Nuclear Cross Section - Macroscopic Cross Section

Macroscopic Cross Section

Nuclear cross sections are used in determining the nuclear reaction rate, and are governed by the reaction rate equation for a particular set of particles (usually viewed as a "beam and target" thought experiment where one particle or nucleus is the "target" and the other is treated as a "beam" ).

For neutron interactions incident upon a thin sheet of material (ideally made of a single type of isotope), the nuclear reaction rate equation is written as:

where:

• : number of reactions of type x, units:
• : neutron beam flux, units:
• : microscopic cross section for reaction, units: (usually barns or cm2).
• : density of atoms in the target in units of
• : macroscopic cross-section

Types of reactions frequently encountered are s: scattering, : radiative capture, a: absorption (radiative capture belongs to this type), f: fission, the corresponding notation for cross-sections being:, etc. A special case is the total cross-section, which gives the probability of a neutron to undergo any sort of reaction .

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 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.