Sum Rule for the Landau Fermi-Liquid Parameters in Metals

Abstract

We have derived an exact sum rule among the Legendre polynomial expansion coefficients of the Landau $f$ function. The relation explicitly depends on both band-structure and phonon-anisotropy effects. It is based on the exclusion principle and correctly takes into account the effects of the long-range self-consistent field. We compare the predictions of the sum rule with the sum of the first few experimentally determined Landau parameters for Na. The results of the comparison are consistent with the existing data.