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 (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.
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 (with scalar r), G(r,t) is a time dependent radial distribution function.
- Hansen, J. P.; McDonald, I. R. (1986). Theory of Simple Liquids. Academic Press.
- van Hove, L. (1954). "Correlations in Space and Time and Born Approximation Scattering in Systems of Interacting Particles". Physical Review. 95 (1): 249. Bibcode:1954PhRv...95..249V. doi:10.1103/PhysRev.95.249.
- G. Vineyard, "Scattering of Slow Neutrons by a Liquid", Phys. Rev. 110, 999-1010 (1958).