Percus–Yevick equation for systems in external fields

The Percus–Yevick equation for the radial distribution function is generalized to the case of external fields and an arbitrary form of the potential of the two-particle interaction. The resulting equation is closed by means of the exact Bogolyubov equation for the single-particle distribution function. An investigation is made of the asymptotic (for large distances) behavior of the solution for the radial distribution function and a virial expansion is found for a lowdensity gas. The equation obtained is used to calculate the shift of the critical temperature of a paramagnetic liquid under the influence of a weak magnetic field.