Cavity correlation function

The cavity correlation function, $y(r_{12})$, is given by

$y(r)\equiv {\mathrm {g} }(r)/e^{-\beta \Phi _{12}(r)}$

where $g(r)$ is the pair distribution function, $\Phi _{12}(r)$ is the pair potential, and $\beta :=1(/k_{B}T)$, where $k_{B}$ is the Boltzmann constant and $T$ is the temperature.