and use the convolution theorem, we obtain which yields Closure relations As both functions, and , are unknown, one needs an additional equation, known as a closure relation. While the OZ equation is purely formal, the closure must introduce some physically motivated approximation. In the low-density limit, the pair correlation function is given by the Boltzmann factor, with and with the pair potential . Closure relations for higher densities modify this simple relation in different ways. The best known closure approximations are: The Percus–Yevick approximation for particles with impenetrable ("hard") core, the hypernetted-chain approximation, for particles with soft cores and attractive potential tails, the mean spherical approximation, the Rogers-Young approximation. The latter two interpolate in different ways between the former two, and thereby achieve a satisfactory description of particles that have a hard core and attractive forces. References External links Statistical mechanics Integral equations