Differential cross section

The cross section is an effective area that quantifies the essential likelihood of a scattering event when an incident beam strikes a target object, made of separate particles. In a completely classical setting, where a particle is nothing more than a hard object, the cross section is the area of the conventional geometric cross section, and expresses the probability of hitting the object with a ray. It is typically denoted σ and measured in units of area.

In scattering experiments, one is often interested in knowing how likely a given event is to occur. However, the rate depends strongly on experimental variables such as the density of the target material, the intensity of the beam, or the area of overlap between the beam and the target material. To control for these mundane differences, one can factor out these variables, resulting in an area-like quantity known as the cross section.

Cross section is associated with a particular event (e.g. elastic collision, a specific chemical reaction, a specific nuclear reaction) involving a certain combination of beam (e.g. light, elementary particles, nuclei) and target material (e.g. colloids, gases, atoms, nuclei). Often there are additional factors that can affect the cross section in complicated ways, such as the energy of the beam.

For a given event, the cross section σ is given by

where

Equivalently, if the target material is a thin slab placed perpendicular to the beam, one may express the cross section in terms of flux:

...
Wikipedia