Dynamic structure factor
In condensed matter physics, the dynamic structure factor (or dynamical structure factor) is a mathematical function that contains information about inter-particle correlations and their time evolution. It is a generalization of the structure factor that considers correlations in both space "and" time. Experimentally, it can be accessed most directly by inelastic neutron scattering or X-ray Raman scattering. The dynamic structure factor is most often denoted formula_1, where formula_2 (sometimes formula_3) is a wave vector (or wave number for isotropic materials), and formula_4 a frequency (sometimes stated as energy, formula_5). It is defined as: Here formula_7 , is called the intermediate scattering function and can be measured by neutron spin echo spectroscopy. The intermediate scattering function is the spatial Fourier transform of the van Hove function formula_8: Thus we see that the dynamical structure factor is the spatial "and" temporal Fourier transform of van Hove's time-dependent pair correlation function. It can be shown (see below), that the intermediate scattering function is the correlation function of the Fourier components of the density formula_10: The dynamic structure is exactly what is probed in coherent inelastic neutron scattering. The differential cross section is : where formula_13 is the scattering  length. The van Hove function. The van Hove function for a spatially uniform system containing formula_14 point particles is defined as: It can be rewritten as: In an isotropic sample "G"("r","t") depends only on the distance "r" and is the time dependent radial distribution function.