Structurefunction

A structure function is a quantity used in physics to describe how the internal structure of a system responds to an external probe. It encapsulates information about the spatial or momentum distribution of its constituents and is extracted from scattering experiments or theoretical models. The term is widely used across disciplines, including particle, nuclear, and condensed matter physics.

In high-energy and nuclear physics, structure functions arise in deep inelastic scattering of leptons off hadrons. The most common examples are F1(x, Q^2) and F2(x, Q^2), which depend on the Bjorken scaling variable x and the squared four-momentum transfer Q^2. These functions reflect the momentum distributions of quarks and gluons inside the nucleon and are related to parton distribution functions. The Q^2 evolution of these functions is governed by perturbative quantum chromodynamics through the DGLAP equations. In the naive quark-parton model, a Callan-Gross relation links F2 and F1 for spin-1/2 constituents, with deviations arising from QCD corrections.

In condensed matter and nuclear scattering, the dynamic structure factor S(q, ω) plays a central role. It is the Fourier transform of the density-density correlation function and describes how a system responds to density perturbations with momentum transfer q and energy transfer ω. S(q, ω) determines differential scattering cross sections for neutrons, photons, or electrons, and its integral over ω yields the static structure factor S(q), which encodes static spatial correlations. Sum rules and the fluctuation-dissipation theorem connect S(q, ω) to response functions and thermodynamic properties.

See also: parton distribution function, structure function in scattering, dynamic structure factor, static structure factor, deep inelastic scattering, DGLAP, Callan-Gross relation.