Radial distribution function

In statistical mechanics, the radial distribution function, (or pair correlation function) ${\displaystyle g(r)}$ 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 ${\displaystyle \rho =N/V}$ is the average number density of particles, then the local time-averaged density at a distance ${\displaystyle r}$ from O is ${\displaystyle \rho g(r)}$. This simplified definition holds for a homogeneous and isotropic system. A more general case will be considered below.

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