Effective two-body interaction in Coulomb Fermi liquids

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Abstract
A simple expression for the effective two-body interaction in a Fermi liquid whose constituents interact via a Coulomb force is derived on the basis of a diagrammatic analysis. The interaction, which is spin dependent, is expressed in terms of the local-field factors and the Lindhard polarizability. It includes the contribution of density fluctuations and spin fluctuations, both longitudinal and transverse. A comparison with other interactions known in the literature is made. A generalization to the two-component Coulomb Fermi liquid is also given. An interesting application concerning the possibility of superconductivity in an electron-hole liquid is pointed out.