# Cross Section (discrete events)

## Description

The cross section is an effective area that quantifies the intrinsic likelihood of a scattering event when an incident beam strikes a target object, made of discrete particles. The cross section of a particle is the same as the cross section of a hard object, if the probabilities of hitting them with a ray are the same. 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 occurs. 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 discrete events involving a beam of particles, the cross section σ is given by the formula shown here.

Related formulas## Variables

σ | cross section of this event (m^{2}) |

n | number density of the target particles (m^{-3}) |

I | particle flux (or intensity) of the incident beam (m^{-2}*s^{-1}) |

A | area of overlap between the beam and the target (m^{2}) |

dW | rate at which the event occurs (s^{-1}) |

dz | thickness of the target material (m) |