A measure of the probability of a specific nuclear reaction occurring, expressed as an effective area.In nuclear and particle physics, the cross section is a measure of the probability that a specific interaction will occur when particles collide. It is expressed as an effective area, typically in units of barns (1 barn = 10^-28 square meters), and represents the 'size' of a target as seen by an incoming projectile. A larger cross section means the reaction is more likely to happen; a smaller one means it is rarer. This concept is central to understanding everything from neutron capture in reactors to the production of heavy particles like the top quark at the Large Hadron Collider.
The concept was introduced in the early 20th century, with the term 'cross section' used in scattering experiments by Ernest Rutherford and his colleagues around 1911–1913 to describe the probability of alpha particles being deflected by gold nuclei.
Imagine firing a beam of particles at a thin foil of target material. The cross section is defined as the ratio of the number of reactions per target nucleus to the number of incoming particles per unit area. It is not a physical size of the nucleus but a quantum-mechanical probability, often influenced by resonances, quantum tunneling, and the energy of the incoming particle. For example, a neutron might have a huge cross section for capture at certain energies due to resonance, making it appear 'large' even though the nucleus itself is tiny.
Cross sections are used to design nuclear reactors, calculate radiation shielding, and estimate production rates of rare particles in colliders, such as the top quark or Higgs boson.
The unit 'barn' was coined during the Manhattan Project as a slang term for 'big as a barn' to describe the unexpectedly large cross section of certain nuclear reactions.
| \sigma | variable | cross section — cross section metre squared |
| \hbar | constant | reduced Planck constant, fundamental quantum of action — reduced planck constant = 1.054571817e-34 joule second |
| G | constant | Newton's gravitational constant, determines strength of gravity — gravitational constant = 6.67430e-11 metre cubed per kilogram per second squared |
| c | constant | speed of light in vacuum, fundamental constant of relativity — speed of light = 299792458 metre per second |
| \propto | operator | proportional to — proportionality |
| τ | variable | optical depth — optical depth |
| n | variable | number density of absorbers — number density per cubic metre |
| σ | variable | cross-section per absorber — cross section square metre |
| l | variable | path length through the medium — length metre |
| C | variable | capture rate of dark matter particles by the star — capture rate per second |
| R | variable | radius of the star — radius metre |
| ρ_χ | variable | mass density of dark matter in the local environment — mass density kilogram per cubic metre |
| m_χ | variable | mass of a single dark matter particle — mass kilogram |
| v | variable | typical relative speed of dark matter particles with respect to the star — velocity metre per second |
| σ | variable | scattering cross-section between dark matter and stellar nucleons — cross section square metre |
| I | variable | Transmitted intensity — intensity watt per square metre |
| I_0 | variable | Incident intensity — intensity watt per square metre |
| σ | variable | Absorption cross-section per absorber — cross section square metre |
| n | variable | Number density of absorbers — number density per cubic metre |
| x | variable | Path length through the medium — length metre |
| σ | variable | Cross section — cross section metre squared |
| E | variable | Energy of the incident particle — energy joule |
| α | variable | Power-law exponent — dimensionless exponent |
| ∝ | operator | Proportional to, up to a constant factor — proportionality |
| \sigma | variable | Cross section — cross section square metre |
| g_1 | variable | Coupling constant of particle 1 — coupling constant joule metre |
| g_2 | variable | Coupling constant of particle 2 — coupling constant joule metre |
| \mu | variable | Reduced mass of the two-particle system — mass kilogram |
| m | variable | Mass scale (typically the mass of the particles) — mass kilogram |





