Analytical solution of the proper integral equations for interaction site fluids

We apply the Wiener-Hopf factorization technique to the Chandler-Silbey-Ladanyi equations with the Percus-Yevick closure for a general fluid composed of hard-sphere interaction sites. We analytically solve these equations for symmetric n-atomic tangent hard-sphere molecules (n≤4), and obtain closed analytical expressions for the equation of state and other thermodynamic properties of the fluid.