Cavity correlation function

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

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle y(r)\equiv 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k_B} is the Boltzmann constant.