Energy Dependence of the Optical Potential for Electrons

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Abstract
An optical potential is constructed for a pair of electrons in a crystal interacting through short-range forces. A formal expression is obtained in the case of interactions at a single site but connecting an arbitrary number of bands. The energy dependence of this potential is determined from numerical calculations for electrons occupying a parabolic energy band. It is found that, regardless of the strength of the effective interaction, for a wide range of densities, the optical potential is nearly independent of energy, but is larger than predicted by a low-density expression which was previously obtained. These results are applied to the theory of ferromagnetism.