Cavity correlation function

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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.