  We use a previously introduced mapping between the continuum percolation
model and the Potts fluid (a system of interacting s-states spins which are
free to move in the continuum) to derive the low density expansion of the pair
connectedness and the mean cluster size. We prove that given an adequate
identification of functions, the result is equivalent to the density expansion
derived from a completely different point of view by Coniglio et al. [J. Phys A
10, 1123 (1977)] to describe physical clustering in a gas. We then apply our
expansion to a system of hypercubes with a hard core interaction. The
calculated critical density is within approximately 5% of the results of
simulations, and is thus much more precise than previous theoretical results
which were based on integral equations. We suggest that this is because
integral equations smooth out overly the partition function (i.e., they
describe predominantly its analytical part), while our method targets instead
the part which describes the phase transition (i.e., the singular part).
