Pair distribution function

The pair distribution function (PDF) describes the distribution of distances between pairs of particles contained within a given volume. Mathematically, if a and b are two particles in a fluid, the PDF of b with respect to a, denoted by ${\displaystyle g_{ab}({\vec {r}})}$ is the probability of finding the particle b at distance ${\displaystyle {\vec {r}}}$ from a, with a taken as the origin of coordinates.

The pair distribution function is used to describe the distribution of objects within a medium (for example, oranges in a crate or nitrogen molecules in a gas cylinder). If the medium is homogeneous (i.e. every spatial location has identical properties), then there is an equal probability density for finding an object at any position ${\displaystyle {\vec {r}}}$:

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