Quasi-particle properties and Cooper pairing in trapped Fermi gases

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The possibility for the particles in a Fermi gas to emit and reabsorb density and spin fluctuations gives rise to an effective mass and to a lifetime of the quasi-particles, as well as to an effective pairing interaction which affect in an important way the BCS critical temperature. We calculate these effects for a spherically symmetric trapped Fermi gas of 1000 particles. The calculation provides insight on the many-body physics of finite Fermi gases and is closely related to similar problems recently considered in the case of atomic nuclei and neutron stars.