sigmatotal

Sigmatotal, typically denoted sigma_tot, is a term used in physics to denote the total cross section of a given scattering process. In particle and nuclear physics, the cross section represents the effective area that characterizes the probability of an interaction between an incident particle and a target.

In two-body scattering, sigma_tot(E) is the sum of the elastic and inelastic cross sections: sigma_tot(E) = sigma_el(E) + sigma_inel(E). The total cross section is related to the forward scattering amplitude through the optical theorem: sigma_tot = (4 pi / k) Im f(0), where k is the wavenumber in the center-of-mass frame and f(0) is the forward scattering amplitude. This relationship connects a measurable quantity to the underlying quantum mechanical scattering process.

Measurement and units: sigma_tot is measured in units of area, commonly barns (1 barn = 10^-28 m^2). It can be determined from integrated differential cross sections or inferred from the forward amplitude via the optical theorem. In high-energy experiments, such as proton-proton or proton-nucleus collisions, sigma_tot is observed as a function of energy and provides important constraints on models of strong interactions and hadronic structure.

Applications: Sigmatotal is used to test theoretical models of particle interactions, to extract information about internal structure such as parton distributions, and to compare results across different experimental setups and energy scales. It also has relevance in cosmic-ray physics and neutrino scattering, where total interaction probabilities influence fluxes and event rates.

Etymology and related concepts: The term combines the Greek letter sigma, commonly used for cross sections, with the word total. Related concepts include sigma_el, sigma_inel, and the broader framework of differential cross sections and the optical theorem.