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===The structure factor===
The second-order correlation function <math>g^{(2)}(\mathbf{r}_{1},\mathbf{r}_{2})</math> is of special importance, as it is directly related (via a [[Fourier transform]]) to the [[structure factor]] of the system and can thus be determined experimentally using [[X-ray diffraction]] or [[neutron diffraction]].<ref>{{cite book | last1 = Dinnebier | first1 = R E | last2 = Billinge | first2 = S J L | title = Powder Diffraction: Theory and Practice | url = https://archive.org/details/powderdiffractio00redi | url-access = limited | publisher = Royal Society of Chemistry | edition = 1st | date = 10 Mar 2008 | pages =
If the system consists of spherically symmetric particles, <math>g^{(2)}(\mathbf{r}_{1},\mathbf{r}_{2})</math> depends only on the relative distance between them, <math>\mathbf{r}_{12} = \mathbf{r}_{2} - \mathbf{r}_{1} </math>. We will drop the sub- and superscript: <math>\textstyle g(\mathbf{r})\equiv g^{(2)}(\mathbf{r}_{12})</math>. Taking particle 0 as fixed at the origin of the coordinates, <math>\textstyle \rho g(\mathbf{r}) d^3r = \mathrm{d} n (\mathbf{r})</math> is the ''average'' number of particles (among the remaining <math>N-1</math>) to be found in the volume <math>\textstyle d^3r</math> around the position <math>\textstyle \mathbf{r}</math>.
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