The Boltzmann collision integral for binary encounters is restricted to rarefied gases and plasmas by the constraint that the mean free path be much larger than the range of interaction. For dense media the two lengths become comparable and a proper account of the mutual influence exerted by one particle on the other during a collision must be taken. There are also other situations involving charged–charged long-range interactions for which this condition is met even in rarefied plasmas. The matter is considered in this work with the solution of the BBGKY (Born, Bogoliubov, Kirkwood, (H. S.) Green, Yvon) equation to determine the joint distribution function for the encountering particles. It is shown, in particular, that for dense gases the results replace the traditional Enskog $\chi $ factor, whereas for plasmas oscillatory phenomena can be driven. The proposed theory constitutes an improvement over the revised Enskog theory (RET) to the extent that it is not restricted to the soft sphere encounters, but valid for any sort of field interaction between colliding particles. Moreover the correlation term replaces the unsuitable restitution coefficient of the RET approach, which is restricted to impact theory. The present material is important for studies in solar and terrestrial physics, which require the sole knowledge of the one particle distribution function, namely gas dynamics and Coulomb plasma research.