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The screening function of an interacting electron gas at high and metallic densities is investigated by many-body perturbation theory. The analysis is guided by a fundamental relation between the compressibility of the system and the zero-frequency small wave-vector screening function (i.e. screening constant). It is shown that the contribution from a graph not included in previous work is essential to obtain the lowest-order correlation correction to the screening constant at high density. Also, this graph gives a substantial contribution to the screening constant at metallic densities. The general problem of choosing a self-consistent set of graphs for calculating the screening function is discussed in terms of a coupled set of integral equations for the propagator, the self-energy, the vertex function, and the screening function. A modification of Hubbard's (1957) form of the screening function is put forward on the basis of these results.
Geldart et al. (Thu,) studied this question.