Universal expansion of three-particle distribution function

A universal, i.e., not dependent on the Hamiltonian of the two-particle interaction, expansion of the equilibrium three-particle distribution function with respect to the two-particle correlation functions is constructed. A diagram technique that permits systematic calculation of the coefficients of this expansion is proposed. In particular, it is established that allowance for the first four orders in the absence of long-range correlations gives the Kirkwood approximation. Corrections to the Kirkwood approximation both in the presence and absence of long-range correlations are found.