Ferromagnetic transition of a two-component Fermi gas of Hard Spheres

We use microscopic many-body theory to analyze the problem of itinerant ferromagnetism in a repulsive atomic Fermi gas of Hard Spheres. Using simple arguments, we show that the available theoretical predictions for the onset of the ferromagnetic transition predict a transition point at a density ($k_F a \sim 1$) that is too large to be compatible with the universal low-density expansion of the energy. We present new variational calculations for the hard-sphere Fermi gas, in the framework of Fermi hypperneted chain theory, that shift the transition to higher densities ($k_F a \sim 1.8$). Backflow correlations, which are mainly active in the unpolarized system, are essential for this shift.