The dielectric function of the electron gas at intermediate densities. I

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Abstract
A first-principles approach for calculating the dielectric function of the uniform electron gas is presented. Developing the Green functions for the response of the system by an equations-of-motion and a perturbation theory for the mass operator, it is shown that the theory can be pushed beyond the existing results without the loss of algebraic tractability. The analysis leads to successive approximations to the mass operator and to the dynamic 'load field correction' whilst making contact with the existing theories in a transparent manner. As the method uses no decoupling approximation but depends upon an algebraic development of the Dyson equation, comparison with diagrammatic theories becomes very easy.