Effective mass, spin fluctuations, and zero sound in liquid3He

Abstract

We have measured and calculated the density and spin-density dynamic structure factors ${S}_{c}(Q,\ensuremath{\omega})$ and ${S}_{I}(Q,\ensuremath{\omega})$ of normal liquid ${}^{3}\mathrm{He}$ as a function of wave vector Q and temperature T. The static spin susceptibility $\ensuremath{\chi}(T)$ and specific heat ${C}_{V}(T)$ are also calculated. These properties all depend upon the effective mass ${m}^{*}(k,\ensuremath{\omega})$ of the Fermi quasiparticles making up the liquid. We use a model in which ${m}^{*}$ peaks near the Fermi surface to ${m}^{*}=2.8,$ the Landau theory effective mass, and decreases toward the bare mass ${m}^{*}=1$ for quasiparticles away from the Fermi energy ${\ensuremath{\epsilon}}_{F}.$ The theory for all the properties may be viewed as Landau theory with an effective mass ${m}^{*}({\ensuremath{\epsilon}}_{k}{)=m}^{*}(k)$ that decreases as the quasiparticle energy ${\ensuremath{\epsilon}}_{k}$ moves away from ${\ensuremath{\epsilon}}_{F}.$ The peaking of ${m}^{*}$ at ${\ensuremath{\epsilon}}_{F}$ is widely predicted in Fermi systems and the aim is to test how important this physical feature is in the dynamics of liquid ${}^{3}\mathrm{He}.$ We find that ${S}_{c}(Q,\ensuremath{\omega})$ and ${S}_{I}(Q,\ensuremath{\omega})$ versus Q and T as well as $\ensuremath{\chi}(T)$ are well reproduced by the model for the same ${m}^{*}(k).$ The ${C}_{V}(T)$ can be reproduced, but a much lower value of ${m}^{*}(k)$ at energies ${\ensuremath{\epsilon}}_{k}$ away from ${\ensuremath{\epsilon}}_{F}$ is required, ${m}^{*}\ensuremath{\simeq}0.5,$ as found in previous calculations of ${C}_{V}(T).$ We conclude that the peaking of ${m}^{*}$ at ${\ensuremath{\epsilon}}_{F}$ is an important physical feature to include in calculations of $S(Q,\ensuremath{\omega})$ and that the quasiparticle model itself is inadequate for ${C}_{V}$ at higher temperatures.