  We study strongly interacting two component Fermi gas near a Feshbach
resonance. By using a ground state energy functional constructed based on
asymptotic limits and Monte Carlo calculations, we calculate the contact,
structure factor, and collective oscillation frequencies in the BCS-BEC
crossover region. The calculated contact and structure factor show excellent
agreements with recent experiments. We compare these results with a standard
mean-field theory and find that the contact is proportional to the square of
superfluid order parameter. Further, we present the chemical potential and the
polytropic index in terms of homogenous energy and the contact.
