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) not equal 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/(ar(e)(2))(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 s(6). (c) 2018 The Author(s). Published by Elsevier B.V.