The screened uniform charge model for nearly-free-electron metals

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Abstract
The charge density due to conduction electrons in a metal is the sum of a uniform density n0 and the change in n0 due to the presence of the ions. We show that n0 contributes to the q not equal 0 matrix elements of the effective potential for electrons. The sum of the ionic potentials Vion(r) of an infinite metal is divergent and the matrix elements of this sum cannot be expressed as a product of a structure factor and a single matrix element. By considering the effects of n0, this divergence can be avoided; the resulting potential Vneut(r-Rj0), when an ion is on the lattice site Rj0 is defined; its screened version Vs,neut(r-Rj0) is shown to have phase shifts whose Friedel sum is zero. We assert that Vs,neut(r) is the potential that should be used in band-structure calculations. The pseudopotential formed from Vs,neut(r) is shown to have zero expectation value at the Fermi energy, and the relation of the band-structure energies E(k) to an absolute scale is derived. For scattering, the model produces results similar to those of Bardeen, and, when various approximations are made, to those of earlier theories which use a potential with phase shifts whose Friedel sum is Z, the valence. The improved accuracy which the model should give is stressed. Simple calculations on lithium, sodium and potassium suggest that the model is reasonable.

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