  In this paper, we study the truncated two-particle correlation function in
particle systems with long range interactions. For Coulombian and soft
potentials, we define and give well-posedness results for the equilibrium
correlations. In the Coulombian case, we prove the onset of the Debye screening
length in the equilibrium correlations, for suitable velocity distributions.
Additionally, we give precise estimates on the effective range of interaction
between particles. In the case of soft potential interaction the equilibrium
correlations and their fluxes in the space of velocities are shown to be
linearly stable.
