Editing Cross section (physics) (section)

{{Short description|Probability of a given process occurring in a particle collision}}
{{Redirect-distinguish|Scattering cross section|Radar cross-section{{!}}Radar scattering cross section}}
{{More footnotes|date=January 2022}}

In physics, the '''cross section''' is a measure of the probability that a specific process will take place in a collision of two particles.  For example, the [[Rutherford scattering|Rutherford cross-section]] is a measure of probability that an [[alpha particle]] will be deflected by a given angle during an interaction with an [[atomic nucleus]]. Cross section is typically denoted {{math|''σ''}} ([[sigma]]) and is expressed in units of area, more specifically in [[barn (unit)|barn]]s. In a way, it can be thought of as the size of the object that the excitation must hit in order for the process to occur, but more exactly, it is a parameter of a [[stochastic process]].

When two discrete particles interact in classical physics, their mutual '''cross section''' is the area [[transversality (mathematics)|transverse]] to their relative motion within which they must meet in order to [[scattering|scatter]] from each other. If the particles are hard [[elasticity (physics)|inelastic]] [[sphere]]s that interact only upon contact, their scattering cross section is related to their geometric size. If the particles interact through some action-at-a-distance force, such as [[electromagnetism]] or [[gravity]], their scattering cross section is generally larger than their geometric size.

When a cross section is specified as the [[Differential of a function|differential]] limit of a function of some final-state variable, such as particle angle or energy, it is called a '''differential cross section''' (see detailed discussion below). When a cross section is integrated over all scattering angles (and possibly other variables), it is called a '''total cross section''' or '''integrated total cross section'''. For example, in [[Rayleigh scattering]], the intensity scattered at the forward and backward angles is greater than the intensity scattered sideways, so the forward differential scattering cross section is greater than the perpendicular differential cross section, and by adding all of the infinitesimal cross sections over the whole range of angles with integral calculus, we can find the total cross section.

Scattering cross sections may be defined in [[nuclear physics|nuclear]], [[atomic physics|atomic]], and [[particle physics]] for collisions of accelerated beams of one type of particle with targets (either stationary or moving) of a second type of particle. The probability for any given reaction to occur is in proportion to its cross section. Thus, specifying the cross section for a given reaction is a proxy for stating the probability that a given scattering process will occur.

The measured [[reaction rate]] of a given process depends strongly on experimental variables such as the density of the target material, the intensity of the beam, the detection efficiency of the apparatus, or the angle setting of the detection apparatus. However, these quantities can be factored away, allowing measurement of the underlying two-particle collisional cross section.

Differential and total scattering cross sections are among the most important measurable quantities in [[nuclear physics|nuclear]], [[atomic physics|atomic]], and [[particle physics]].

With light scattering off of a particle, the '''cross section''' specifies the amount of optical power scattered from light of a given irradiance (power per area). Although the cross section has the same units as area, the cross section may not necessarily correspond to the actual physical size of the target given by other forms of measurement. It is not uncommon for the actual cross-sectional area of a scattering object to be much larger or smaller than the cross section relative to some physical process. For example, [[plasmonic nanoparticles]] can have light scattering cross sections for particular frequencies that are much larger than their actual cross-sectional areas.