The imaginary part of the transverse dielectric tensor has been calculated for sodium using a two-band model and including both phonons and the interactions between conduction electrons in the random-phase approximation. It is found that the resulting expression reduces to the Hopfield dielectric constant for the case of an electron gas in a perturbing crystal potential. Reasonable agreement with N. V. Smith's data has been found in the range of photon energies 0.5-3.0 eV. However, at higher energies the agreement is not as good, since many-body effects become more important in this region.
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Karakashian et al. (1971) studied this question.
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