Scattering

Scattering is a process in physics in which waves or particles are redirected through interaction with matter, other particles, or a field. The outgoing radiation or particles may differ from the incoming ones in direction, energy, or internal state. Examples include light scattered by atmospheric molecules, neutrons scattered by solids, and collisions between subatomic particles. Measurements of scattering reveal both the structure of a target and the interactions governing its behavior. (psg.gsfc.nasa.gov)

Physical description and classifications

A scattering experiment typically directs a beam toward a target and measures the outgoing particles or waves. Relevant observables include scattering angle, energy transfer, and polarization. The results depend on the incident beam, the target’s properties, and the interaction between them. Scattering need not involve mechanical contact: electromagnetic forces can deflect charged particles, while light can be scattered through the induced electrical response of a molecule. (indico.cern.ch)

In elastic scattering, the total kinetic energy of the colliding system is conserved and its internal states remain unchanged. An individual projectile may nevertheless lose energy through target recoil. In inelastic scattering, energy is exchanged with internal excitations or other degrees of freedom. In optical terminology, elastic scattering ordinarily means that the scattered light has the same frequency as the incident light, neglecting recoil and motion-induced shifts. (ocw.mit.edu)

Coherent scattering retains phase relationships that allow contributions from different scattering centers to produce interference. The resulting pattern carries information about their arrangement. Diffraction from a crystal is an important example: waves scattered by its regularly spaced constituents reinforce one another in particular directions. Coherence and elasticity describe different properties and should not be treated as synonymous. (iucr.org)

Cross sections and angular distributions

The principal quantitative measure is the cross section, an effective area expressing the strength or likelihood of a specified interaction. It is not necessarily the target’s geometric area. Cross sections depend on quantities such as incident energy and the selected final state. A commonly used unit in nuclear and particle physics is the barn, equal to $10^{-28}\,\mathrm{m^2}$. (opendata.cern.ch)

The differential cross section $d\sigma/d\Omega$ describes scattering into a unit solid angle around a particular direction. Integrating over outgoing directions gives the cross section for that scattering channel:

Measurements may also resolve outgoing energy, producing cross sections differential in both energy and angle. Angular distributions distinguish strongly forward-directed scattering from more broadly distributed scattering and provide information beyond a single total value. (opendata.cern.ch)

Scattering of light

Rayleigh scattering describes the small-scatterer limit, where the relevant dimensions are much smaller than the wavelength. Away from resonances, its strength varies approximately as $\lambda^{-4}$. Molecules in the Earth’s atmosphere therefore scatter shorter visible wavelengths more strongly than longer ones. This contributes to the blue daytime sky; near sunrise or sunset, the longer atmospheric path removes more blue light from the direct solar beam. (psg.gsfc.nasa.gov)

Mie theory describes electromagnetic scattering by spheres and includes Rayleigh behavior as a limiting case. It is especially useful for particles comparable to or larger than the wavelength. Atmospheric aerosols and cloud droplets can produce pronounced forward scattering and weaker wavelength dependence than molecular Rayleigh scattering, helping explain the whitish appearance of clouds and haze. Particle size, composition, and shape determine the detailed response. (acd-ext.gsfc.nasa.gov)

In Compton scattering, a photon exchanges energy and momentum with an electron. A photon scattered by an initially stationary free electron generally loses energy, whereas energetic electrons can transfer energy to photons. This interaction is important in high-energy radiation detection and astrophysics. (ntrs.nasa.gov)

Quantum scattering theory

In quantum mechanics, scattering is described through incoming and outgoing components of a wave function. For a simple elastic process involving a short-range potential, the distant scattered wave is approximately spherical. Its direction-dependent coefficient is the scattering amplitude, $f(\theta,\phi)$. With the conventional normalization,

The amplitude contains phase information, whereas the cross section describes the measurable angular intensity. (ocw.mit.edu)

Calculations may use partial-wave expansions, which separate angular-momentum contributions, or the Born approximation, which treats the interaction perturbatively. Their validity depends on the potential, incident energy, and interaction strength. These methods connect a theoretical interaction model to observable scattering patterns. (ocw.mit.edu)

Structural measurements and historical importance

X-rays scatter from the electronic distribution of matter. In X-ray crystallography, interference between contributions from different atoms yields reflections whose intensities depend on the structure factor. Analysis of these measurements provides information about atomic positions and electron density. (iucr.org)

Neutrons provide complementary information because their scattering varies between nuclei and isotopes, and their magnetic properties make them sensitive to magnetic order. Inelastic neutron scattering measures excitations and motions, including lattice vibrations associated with phonons. Electron diffraction likewise probes structure, although strong multiple scattering can complicate interpretation. (nist.gov)

Scattering also transformed understanding of the atom. In 1911, Ernest Rutherford interpreted alpha-particle scattering measurements as evidence for a small, concentrated atomic nucleus. Later, deep inelastic scattering became a means of investigating nucleon structure, extending the use of scattering from atomic architecture to the constituents of matter. (nobelprize.org)