Nuclear cross section


The nuclear cross section of a nucleus is used to describe the probability that a nuclear reaction will occur. 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 is the barn, which is equal to 10−28 m² or 10−24 cm². Cross sections can be measured for all possible interaction processes together, in which case they are called total cross sections, or for specific processes, distinguishing elastic scattering and inelastic scattering; of the latter, amongst neutron cross sections the absorption cross sections are of particular interest.
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.
Typical nuclear radii are of the order 10−14 m. Assuming spherical shape, we therefore expect the cross sections for nuclear reactions to be of the order of πr ² or 10−28 m². Observed cross sections vary enormously - for example, slow neutrons absorbed by the reaction show a cross section much higher than 1,000 barns in some cases, while the cross sections for transmutations by gamma-ray absorption are in the region of 0.001 barn.

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.
For neutron interactions incident upon a thin sheet of material, the nuclear reaction rate equation is written as:
where:
Types of reactions frequently encountered are s: scattering, : radiative capture, a: absorption, 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 as the proportionality constant between a neutron flux incident on a piece of material and the number of reactions that occur in that material. The distinction between macroscopic and microscopic cross-section is that the former is a property of a specific lump of material, while the latter is an intrinsic property of a type of nuclei.