A scattering view of the Bogoliubov-de Gennes equations

We advocate the use of the T -matrix of the pair potential to study the properties of ultra-cold Fermi gases in the mean-field approximation. Our approach does not require renormalization procedures even in the limit of contact interaction, and it provides a rigorous definition of the range of the potential. We also rewrite the Bogoliubov-de Gennes equation for the pairing function as a function of the T-matrix, and use it to investigate finite-range effects on the main thermodynamic observables in a gas of Li-6 atoms at unitarity, calculating the pair potential with ab initio quantum chemical methods.