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Concept
Dynamic structure factor
Summary
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 (sometimes ) is a wave vector (or wave number for isotropic materials), and a frequency (sometimes stated as energy, ). 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 :
The dynamic structure is exactly what is probed in coherent inelastic neutron scattering. The differential cross section is :
where is the scattering length.
Official source
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