We investigate the properties of a trapped two-component, Fermi gas near the unitary limit regime. The bulk properties are discussed through a quasi-linear approximation with a medium dependent effective interaction. The obtained ground state energy for the unitary fermion system is in good agreement with existing theoretical predictions as well as experimental results. Within the framework of hydrodynamics, the radial and axial frequencies of the breathing modes are analyzed in detail. Applied to the cigar shaped harmonic trap, the theoretical results are reasonably consistent with the experimental measurements.
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