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.
The dynamic structure factor is most often denoted, where is a wave vector, and a frequency. 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, that the intermediate scattering function is the correlation function of the Fourier components of the density :
The dynamic structure is exactly what is probed in coherent inelastic neutron scattering. The differential cross section is :
where is the scattering length.

The van Hove function

The van Hove function for a spatially uniform system containing point particles is defined as:
It can be rewritten as:
In an isotropic sample G depends only on the distance r and is the time dependent radial distribution function.