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 >k_F) 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 /r_e, where r_e the effective range. If the scattering length is large and one includes the effects of a fixed value of r_e ≠ 0, n (k) is almost universal for momenta k up to about 2 /r_e. However, n (k) can not be approximated by a zero-range model for momenta k greater than about 1 / (a r_e²)^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.