  We study the ground state properties of interacting Fermi gases in the dilute
regime, in three dimensions. We compute the ground state energy of the system,
for positive interaction potentials. We recover a well-known expression for the
ground state energy at second order in the particle density, which depends on
the interaction potential only via its scattering length. The first proof of
this result has been given by Lieb, Seiringer and Solovej. In this paper we
give a new derivation of this formula, using a different method; it is inspired
by Bogoliubov theory, and it makes use of the almost-bosonic nature of the
low-energy excitations of the systems. With respect to previous work, our
result applies to a more regular class of interaction potentials, but it comes
with improved error estimates on the ground state energy asymptotics in the
density.
