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

Quantum Bose and Fermi gases with large negative scattering length in the 2-body S-matrix approximation