Two-component Fermi Gas in a Harmonic Trap

We consider a mixture of two-component Fermi gases at low temperature. The density profile of this degenerate Fermi gas is calculated under the semiclassical approximation. The results show that the fermion-fermion interactions make a large correction to the density profile at low temperature. The phase separation of such a mixture is also discussed for both attractive and repulsive interatomic interactions, and the numerical calculations demonstrate the existance of a stable temperature region Tc1 < T < Tc2 for the mixture. In addition, we give the critical temperature of the BCS-type transition in this system beyond the semiclassical approximation.