The ground state energy and pairing gap of the interacting Fermi gases calculated by the ab initio stochastic method are compared with those estimated from the Bardeen-Cooper-Schrieffer pairing Hamiltonian. We discuss the ingredients of this Hamiltonian in various regimes of interaction strength. In the weakly interacting $(1∕a{k}_F⪡0)$ regime the BCS Hamiltonian should describe Landau quasiparticle energies and interactions, on the other hand, in the strongly pairing regime, that is, $1∕a{k}_F\gtrsim 0$, it becomes part of the bare Hamiltonian. However, the bare BCS Hamiltonian is not adequate for describing atomic gases in the regime of weak to moderate interaction strength $-\infty <1∕a{k}_F<0$ such as $a{k}_F\sim -1$.

• Received 12 March 2006

DOI:https://doi.org/10.1103/PhysRevB.73.212502