Spatial correlation of conduction electrons in a metal with a complicated geometry of the Fermi surface

The 'density-density' correlation function (CF) of conduction electrons in a metal is investigated. It is shown that the asymptotic behaviour of the CF depends on the shape and the local geometry of the Fermi surface (FS). In particular, the exponent of the power law which describes the damping of Friedel oscillations at r to infinity (-4 for an isotropic Fermi gas) is determined by the local geometry of the FS. The applications of the results obtained to calculations of the CF in a metal near the electron topological transition and of the RKKY exchange integral are considered as well.