Finite Temperature Equilibrium Properties of LiquidHe3in Fermi Liquid Theory

Abstract

Landau's Fermi liquid theory is used to obtain expressions for the respective ${T}^{3}$ and ${T}^{2}$ terms in lowtemperature expansions of the specific heat and magnetic susceptibility of liquid ${\mathrm{He}}^{3}$ at a temperature $T$. Such a calculation is essential toward checking the internal consistency of the Fermi liquid theory above 0.05\ifmmode^\circ\else\textdegree\fi{}K; but previous authors have considered only the zero-temperature limit when working with the Landau parameter, $f$. Coefficients of the finite-temperature corrections derived here are specific functions of $f$ evaluated on the Fermi surface. Existing experimental data on the pressure dependence of the sound velocity, specific heat, and magnetic susceptibility may be used to assign numerical values to these derivatives under the assumption that $f$ depends only on|k-k\ensuremath{'}|. This method of estimation is believed to place an upper limit to the magnitude of the ${T}^{3}$ term in the specific heat; and its resulting value is more than sufficient to account for the specific heat's deviating from linearity below 0.05\ifmmode^\circ\else\textdegree\fi{}K. The strong curvature in the specific heat versus temperature curve above 0.05\ifmmode^\circ\else\textdegree\fi{}K is thus concluded to be consistent with the Fermi liquid theory. The ${T}^{2}$ term in the magnetic susceptibility contains the same function as occurs in the ${T}^{3}$ term for the specific heat plus an additional correction related to derivatives of the spin-dependent part of $f$. A reasonable amount of accuracy is expected in the numerical estimate of this latter term. Assuming this to be the case, this theory is in accord with the susceptibility data of Meyer et al. together with the specific-heat data of Brewer et al. or Fairbank et al., but it cannot reconcile the specific heat data of Wheatley et al. with any existing susceptibility measurements.