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We compute the shear viscosity of a superfluid atomic Fermi gas in theunitarity limit. The unitarity limit is characterized by a divergent scatteringlength between the atoms, and it has been argued that this will result in avery small viscosity. We show that in the low temperature T limit the shearviscosity scales as xi^5/T^5, where the universal parameter 'xi' relates thechemical potential and the Fermi energy, mu=xi E_F. Combined with the hightemperature expansions of the viscosity our results suggest that the viscosityhas a minimum near the critical temperature T_c. A naive extrapolationindicates that the minimum value of the ratio of viscosity over entropy densityis within a factor of ~ 5 of the proposed lower bound hbar/(4\pi k_B).

Shear viscosity of a superfluid Fermi gas in the unitarity limit