Finite-range effects in dilute Fermi gases at unitarity

Abstract

We develop a theoretical method going beyond the contact-interaction approximation frequently used in mean-field theories of many-fermion systems, based on the low-energy $T$ matrix of the pair potential to rigorously define the effective radius of the interaction. One of the main consequences of our approach is the possibility to investigate finite-density effects, which are outside the range of validity of approximations based on $\ensuremath{\delta}$-like potentials. We apply our method to the calculation of density-dependent properties of an ultracold gas of ${}^{6}$Li atoms at unitarity, whose two-body interaction potential is calculated using ab initio quantum chemistry methods. We find that density effects will be significant in ultracold gases with densities 1 order of magnitude higher than those attained in current experiments.