Pressure Dependences of the Transport Coefficients of LiquidHe3and the Spin-Fluctuation Theory

Abstract

The observed pressure dependences of the low-temperature spin diffusion $D$, thermal conductivity $K$, and shear viscosity $\eta$ of liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are interpreted in this paper on the basis of Rice's recent spin-fluctuation theory. With regard to this theory, some new theoretical expressions are obtained: With the use of a more realistic model for the spin-fluctuation weight function, improved calculations are obtained for the limiting low-temperature values ${\alpha }_K$, ${\alpha }_D$, and ${\alpha }_{\eta }$, respectively, of the quantities $\frac{1}{\mathrm{KT}}$, $\frac{1}{D{T}^2}$, $\frac{1}{\eta T^2}$. The effects of longitudinal spin fluctuations, neglected previously, are also included. Within the bound of experimental error, the phenomenological pressure dependence predicted by theory is in good qualitative agreement with experiment. Moreover, considerably improved quantitative agreement is furnished by the improved calculations of ${\alpha }_K$, ${\alpha }_D$, and ${\alpha }_{\eta }$.