Singularities in Forward Multiparticle Scattering Amplitudes and the S-Matrix Interpretation of Higher Virial Coefficients

The role of singular forward multiparticle scattering amplitudes in S-matrix formulas for the higher virial coefficients is studied in detail. It is shown that by means of a simple limiting process one can give a precise, unambiguous meaning to the traces over on-shell scattering amplitudes which appear in our previous formulas for the virial coefficients. The general arguments, in which we maintain a reasonable level of rigor, are supported by explicit calculations for the third and fourth virial coefficients. Also, the angular momentum expansion used in earlier work is shown to converge.