[1][2] The concept of a nuclear cross section can be quantified physically in terms of "characteristic area" where a larger area means a larger probability of interaction.
The standard unit for measuring a nuclear cross section (denoted as σ) is the barn, which is equal to 10−28 m2, 10−24 cm2 or 100 fm2.
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.
Typical nuclear radii are of the order 10−15 m. Assuming spherical shape, we therefore expect the cross sections for nuclear reactions to be of the order of
Observed cross sections vary enormously: for example, slow neutrons absorbed by the (n,
) reaction show a cross section much higher than 1,000 barns in some cases (boron-10, cadmium-113, and xenon-135), while the cross sections for transmutations by gamma-ray absorption are in the region of 0.001 barn.
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", which is typically at rest, and the other is treated as a "beam", which is a projectile with a given energy).
For particle interactions incident upon a thin sheet of material (ideally made of a single isotope), the nuclear reaction rate equation is written as: where: Types of reactions frequently encountered are s: scattering,
, which gives the probability of a neutron to undergo any sort of reaction (
Formally, the equation above defines the macroscopic cross-section (for reaction x) as the proportionality constant between a particle 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.