Thermal Conductivity of Fermi Particle Systems

Abstract

An interpolation formula for the coefficient of thermal conductivity valid in the entire region of temperature is derived for Fermi gases on the basis of the general quantum-statistical expression in terms of the time-dependent correlation function. The formula for the conductivity gives the temperature dependence of 1/T in the extremely degenerate case, and leads to an expression similar to that of Uehling for the first correction due to the Fermi statistics in the slightly degenerate case, and to the Enskog-Chapman theory in the classical limit. The behavior of the conductivity in the strongly degenerate case is clarified by making use of the S-wave approximation. It is shown that the minimum of the conductivity occurs at the temperature 0.164 times as large as the degeneracy temperature. The results of calculations are used to discuss the experiment by Anderson et al. on the liquid He3 by employing Landau's theory of Fermi liquid. If the effective mass and the degeneracy temperature are taken as m = 2.34m0 and Tc = 2.13°K, which are consistent with recent experiments on the specific heat and the mass density, then a good agreement is obtained oblow beout 0.07°K by assuming a = 3.43 ×10-8 cm for the scattering amplitude describing the collision between quasi-particles.