Self-consistent nonlocal linear-response theory of a relativistic electron gas

The displaced charge in an initially homogeneous electron gas due to a weak perturbing potential as calculated by March and Murray was generalized to include relativistic effects by Baltin and March. This latter result is here used to study the relativistic corrections to the static Lindhard dielectric function. An analytic generalization of the Lindhard function to the second order in the Compton wavelength is presented.