Integral equations for radial distribution function with effective allowance for long-range interaction

New integral equations for radial distribution function are obtained on the basis of the conditions for generating functionals. The first equation generalises the well-known parametric integral equations in which the direct correlation function is a linear combination of the Percus–Yevick and hyper-netted-chain direct correlation functions. It is shown that there is no available approximation for the critical region between these approximations. Choosing the generating functional of a special form the second equation for the radial distribution function is derived. This equation is suitable for the correct description of the fluid equilibrium properties near the critical point as well as far from it. The equation of state connected with this integral equation is investigated in the critical, gaseous and intermediate regions. The question about universality of the critical behaviour is discussed.