Specific Heat of a Normal Fermi Liquid. I. Landau-Theory Approach

The contribution of small-momentum-transfer processes to the T³ lnT term in the specific heat of a normal Fermi liquid is considered using Landau theory, and is evaluated exactly in terms of Landau parameters. This contribution is shown to be due to a term in the quasiparticle interaction, f_→p, →p+→q, which varies as (^p·^q)² when →q→0; the physical process responsible for this behavior is the repeated scattering of quasiparticle-quasihole pairs. It is well known that for the two-body problem the interaction energy, while not, in general, equal to the real part of the forward-scattering amplitude, may be expressed in terms of the scattering amplitude. We take over the results for the two-body problem and apply them to a quasi-particle-quasihole pair. This gives an expression for f_→p,→p+→q in terms of the quasiparticle-quasihole scattering amplitude, which, since →q is small, may be expressed in terms of Landau parameters. We apply our results to liquid He³ at low pressure.