Bulk and collective properties of a dilute Fermi gas in the BCS-BEC crossover

We investigate the zero-temperature properties of a dilute two-component Fermi gas with attractive interspecies interaction in the BCS-BEC crossover. We build an efficient parametrization of the energy per particle based on Monte Carlo data and asymptotic behavior. This parametrization provides, in turn, analytical expressions for several bulk properties of the system such as the chemical potential, the pressure and the sound velocity. In addition, on the basis of a local polytropic equation of state, we determine the collective modes of the Fermi gas under harmonic confinement in the framework of the hydrodynamic theory. The calculated collective frequencies are compared to experimental data on confined vapors of $^6$Li atoms and with other theoretical predictions.