  We present a new approach to derive the connectivity properties of pairwise
interacting n-body systems in thermal equilibrium. We formulate an integral
equation that relates the pair connectedness to the distribution of nearest
neighbors. For one-dimensional systems with nearest-neighbor interactions, the
nearest-neighbor distribution is, in turn, related to the pair correlation
function g through a simple integral equation. As a consequence, for those
systems, we arrive at an integral equation relating g to the pair
connectedness, which is readily solved even analytically if g is specified
analytically. We demonstrate the procedure for a variety of pair-potentials
including fully penetrable spheres as well as impenetrable spheres, the only
two systems for which analytical results for the pair connectedness exist.
However, the approach is not limited to nearest-neighbor interactions in one
dimension. Hence, we also outline the treatment of external fields and
long-ranged interactions, and we illustrate how the formalism can applied to
higher-dimensional systems using the three-dimensional ideal gas as an example.
