Dynamic structure factor

In condensed matter physics, the dynamic 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. In condensed matter physics, the dynamic 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 S ( k → , ω ) {displaystyle S({vec {k}},omega )} , where k → {displaystyle {vec {k}}} (sometimes q → {displaystyle {vec {q}}} ) is a wave vector (or wave number for isotropic materials), and ω {displaystyle omega } a frequency (sometimes stated as energy, ℏ ω {displaystyle hbar omega } ). It is defined as: Here F ( k → , t ) {displaystyle F({vec {k}},t)} , 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 G ( r → , t ) {displaystyle G({vec {r}},t)} : 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 ρ {displaystyle ho } : The dynamic structure is exactly what is probed in coherent inelastic neutron scattering. The differential cross section is : where a {displaystyle a} is the scattering length. The van Hove Function for a spatially uniform system containing N {displaystyle N} point particles is defined as: