Viscosity of Fermi Particle Systems

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Abstract
The quantum-statistical expression for the viscosity coefficient in terms of time correlation function is calculated for Fermi gases, and an interpolation formula valid in the entire region of temperature is derived. The formula for the viscosity gives the temperature dependence of T-2 in the extremely degenerate case, and leads to Uehling's expression for the quantum correction in the slightly degenerate case, and to the Enskog-Chapman theory in the classical limit. The behaviour in the intermediate temperature region between the extremely and slightly degenerate cases is determined with numerical calculation by using the S-wave approximation. It is shown that the minimum of the viscosity occurs at about 0.6 Tc, Tc being the degeneracy temperature. These results are used to discuss Zinov'eva's experiments on the viscosity of liquid He3 by employing Landau's theory of Fermi liquid. The effective mass and the degeneracy temperature are determined from recent experiments on the heat capacity, as m = 2.34mo and TC=2.13 °K. A good agreement is obtained below about T = 0.6 °K by assuming a = 1.158 ×10-8 cm for the scattering amplitude describing the collision between quasi-particles.

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