The theory of cluster expansions is studied by a new method. A general procedure for obtaining the thermal average of a many-body function as a series in powers of density is derived. A recipe based on the Daker-Hausdorff theorem for reducing quantum thermal averages to their classical analogs is also described. These results are used to express the slow neutron cross sections of imperfect gases as power series in molecular density. Formulas are given for the leading contributions to both elastic and inelastic scattering. (auth)