In nuclear physics it is conventional to consider the impinging particles as point particles having negligible diameter. Cross sections can be computed for any sort of process, such as capture scattering, production of neutrons, etc. In many cases, the number of particles emitted or scattered in nuclear processes is not measured directly; one merely measures the attenuation produced in a parallel beam of incident particles by the interposition of a known thickness of a particular material. The cross section obtained in this way is called the total cross section and is usually denoted by a σ or σT.
The typical nuclear radius is of the order of 10−12 cm. We might therefore expect the cross sections for nuclear reactions to be of the order of or roughly 10−24 cm2 and this unit is given its own name, the barn, and is the unit in which cross sections are usually expressed. Actually the observed cross sections vary enormously. Thus for slow neutrons absorbed by the (n, gamma) reaction the cross section in some cases is as much as 1,000 barns, while the cross sections for transmutations by gamma-ray absorption are in the neighborhood of 0.001 barns.
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" [typically at rest] and the other is treated as a "beam" [projectile with a given energy]).
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:
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.