The analytic solution of the Percus-Yevick and mean spherical equations for potentials of finite range

The Percus-Yevick and mean spherical approximations (MSA) for an arbitrary smooth potential of finite range are solved in closed form. The solution is in the form of an infinite series whose coefficients involve only definite integrals of functions of the potential. The method of solution involves an extension of the method of Baxter and the theory of Dirichlet series. For the case of the MSA with a Yukawa potential, it is possible to relax the finite range condition, resum the series explicitly and recover the known solution.