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The ground state energy of the free electron gas is calculated using the Rayleigh-Schrödinger variational method with the wave function ψ=DΠi<jf(xij) where D is a determinant of plane waves and f(xij) a correlation function. Consideration of the wave function in terms of the collective coordinates pk' the Fourier components of the density, suggests an accurate approximation for the energy integral which is then evaluated over the coordinates of the particles so that the use of subsidiary conditions is avoided. Effects omitted in the random phase approximation are included and the final results extend continuously over plasma and particle modes and should be valid in the range of densities encountered in real metals. The results agree closely with those of Nozières and Pines, and of Hubbard obtained by more elaborate methods.
T. Gaskell (Thu,) studied this question.
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