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. This work shows that $n(k)$ can not be approximated by a zero-range model for momenta $k$ greater than about $1/(a r_e^2)^{1/3}$, where $a$ is the scattering length, and $r_e$ the effective range. However, if the scattering length is large and one includes the effects of a fixed value of $r_e\ne0$, $n(k)$ is universal for momenta $k$ up to about $2/r_e$. An accurate relation between the energy of a two component Fermi-gas and an integral involving the density is derived. The short separation distance, $s$, behavior of the pair density is shown to vary as $s^6$.