As a first step towards understanding many-body effects on the properties of conduction electrons in a metal, an often used model is that of an electron gas against a uniform, neutralizing positive background. Most treatments of even this model problem make simplifying assumptions about the correlations between electrons in order to get solvable equations. In particular, the correlations between antiparallel spins are often neglected since they make the many-body equations nonlinear and, therefore, difficult to handle. On the other hand, these correlations may be expected to influence strongly many properties of the system, particularly those that depend on high momentum transfers. This paper attempts to remedy this shortcoming in the application of many-body theory to an electron gas by seeking a variational treatment of the full nonlinear equations and derives expressions for the dielectric function and the paramagnetic spin susceptibility which express a wide range of electrical and magnetic properties of the system. Our results show, on comparison with previous treatments neglecting antiparallel spin correlation, that inclusion of these correlations has the expected effect of enhancing the spin susceptibility and lowering the compressibility of the system. Further, our technique of working consistently with the complete defining equations may find applicability in a wider class of problems; a specific example is the charged-boson system.

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