Abstract
The local-field correction of a homogeneous interacting electron gas with positive background (jellium) is studied within the framework of an extended random-phase approximation in which exchange and self-energy effects are consistently taken into account. An iterative solution of the ensuing integral equation for the polarization propagator is derived by using a method which leads to a continued-fraction expansion for the local-field correction. When truncated at first order this expansion gives results in agreement with approximations which have been obtained using other methods. The long-wavelength limit is studied in detail, the first- and second-order diagrams are explicitly evaluated, and it is shown that the second-order terms do not remove the singularity in the first-order local-field correction.
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