Energy dependence of the effective mass in liquid³He

Abstract

The striking behavior of the specific heat of liquid³He as function of temperature at low temperatures requires the effective massm* to change rapidly with temperature; this can be translated into a rapid variation with energy,m*/m dropping from itsE=0 value to ∼1 over the temperature range ≲0.5 K. We explore this effect in a model in which the enhancement of the effective mass is due to coupling to spin fluctuations. At very lowT≲50 mK, the variation in specific heat results fromT ³ lnT terms. The free energy, on the other hand, does not containT ² lnT terms in its dependence on the magnetic field, implying that the susceptibility, which is essentiallym*/(1+F ^a₀ ), also does not have such logarithmic terms. Consequently, ifm* varies with energy, so mustF ^a₀ , so as to leave the susceptibility free of this rapid variation. The rough constancy ofm*/(1+F ^a₀ ) seems empirically to hold to higher energies and temperatures. Ifm*/m drops, with increasing energy, to unity, the spin-fluctuation theory, which is described in terms of Landau parameters at the Fermi surface, goes over into the paramagnon theory. The rapid change with energy of the effective interactions can be understood within the framework of response theory as a “shaking off” of the relevant collective modes with increasing frequency of the imposed oscillations. The changes in effective interactions have consequences for the interpretation of experiments involving inelastic neutron scattering from liquid³He.