  We study both Bose and Fermi gases at finite temperature and density in an
approximation that sums an infinite number of many body processes that are
reducible to 2-body scatterings. This is done for arbitrary negative scattering
length, which interpolates between the ideal and unitary gas limits. In the
unitary limit, we compute the first four virial coefficients within our
approximation. The second virial coefficient is exact, and we extend the
previously known result for fermions to bosons, and also for both bosons and
fermions for the upper branch on the other side of unitarity (infinitely large
positive scattering length). Assuming bosons can exist in a meta-stable state
before undergoing mechanical collapse, we map out the critical temperatures for
strongly coupled Bose-Einstein condensation as a function of scattering length.
