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The optical conductivity is evaluated for interband transitions between a flat valence band and a parabolic conduction band. The conduction band is filled with electrons to a Fermi energy ₅. The conductivity is calculated assuming that the electron-hole interaction is attractive, static, and short range. The final-state interactions between the electron and hole cause a divergence in the conductivity at the interband threshold. This divergence appears to go as a power law. For this case of an infinite hole mass, the exciton binding energy vanishes, since the singularity in the scattering amplitude occurs just at threshold.
G. D. Mahan (Wed,) studied this question.