Landau's Model of LiquidHe3

Abstract

Landau's model of liquid ${\mathrm{He}}^3$ as a Fermi liquid is studied with regard to its lowest temperature properties. Primary stress is laid on the coefficient of thermal expansion. The spectra used by Abrikosov and Khalatnikov, the perfect-gas type and "bubble" type, are shown to give a positive coefficient of thermal expansion, in contradiction with experiment. An alternative simple spectrum is suggested which can give a negative coefficient of thermal expansion, namely $\Delta +\frac{p^2}{2m^{*}}$. In addition, the existence of a negative coefficient of thermal expansion is shown to imply a strong temperature dependence of the energy spectrum, which may cause a sharp deviation of the heat capacity curve from the perfect-gas type, similar to the deviations observed in liquid ${\mathrm{He}}^3$.