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We analyze strongly interacting Fermi gases in the unitary regime by considering the generalization to an arbitrary number N of spin- 1 2 fermion flavors with Sp (2N) symmetry. For N→ this problem is exactly solved by the Bardeen-Cooper-Schrieffer-Bose-Einstein condensate mean-field theory, with corrections small in the parameter 1 N. The large- N expansion provides a systematic way to determine corrections to mean-field predictions, allowing the calculation of a variety of thermodynamic quantities at (and in proximity to) unitarity, including the energy, the pairing gap, and the upper-critical polarization (in the case of a polarized gas) for the normal to superfluid instability. For the physical case of N=1, among other quantities, we predict in the unitarity regime, the energy of the gas to be ξ=0.28 times that for the noninteracting gas and the pairing gap to be 0.52 times the Fermi energy. © 2007 The American Physical Society.

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Physical Review A - Atomic, Molecular, and Optical Physics