Radial distribution function

In statistical mechanics, the radial distribution function, (or pair correlation function) in a system of particles (atoms, molecules, colloids, etc.), describes how density varies as a function of distance from a reference particle.

If a given particle is taken to be at the origin O, and if is the average number density of particles, then the local time-averaged density at a distance from O is . This simplified definition holds for a homogeneous and isotropic system. A more general case will be considered below.