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, where \vec{k} (sometimes \vec{q}) is a wave vector (or wave number for isotropic materials), and \omega a frequency (sometimes stated as energy, \hbar\omega). It is defined as: Here, 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 : 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 \rho: The dynamic structure is exactly what is probed in coherent inelastic neutron scattering. The differential cross section is : where a is the scattering length.

The van Hove function

The van Hove function for a spatially uniform system containing N point particles is defined as: It can be rewritten as: