Non-universal and universal aspects of the large scattering length limit

The momentum density, n(k) of interacting many-body Fermionic systems is studied (for k>kF) using examples of several well-known two-body interaction models. It is shown that n(k) can be approximated by a zero-range model for momenta k less than about 0.1/re, where re the effective range. If the scattering length is large and one includes the effects of a fixed value of re≠0, n(k) is almost universal for momenta k up to about 2/re. However, n(k) can not be approximated by a zero-range model for momenta k greater than about 1/(are2)1/3, where a is the scattering length, and if one wishes to maintain a sum rule that relates the energy of a two component Fermi-gas to an integral involving the density. We also show that the short separation distance, s, behavior of the pair density varies as s6.