  Dynamical mean-field approximation with explicit pairing is utilized to study
the properties of a two-component Fermi gas at unitarity. The problem is
approximated by the lattice Hubbard Hamiltonian, and the continuum limit is
realized by diluting the lattice. We have found that at zero temperature the
predictions of this theory for the energy and the pairing gap agree remarkably
well with the results of full numerical Monte-Carlo simulations. Investigating
the evolution of the system with temperature we identify the existence of a
second order phase transition associated with a jump in the heat capacity and
the collapse of the pairing gap.
