The Hulth\'en potential has been widely used to describe a screened Coulomb potential. We give the first analytical expression of the complex dielectric function of the associated Wannier excitons, which includes the contributions of all bound and unbound states exactly. This expression will greatly simplify calculations of the optical properties of bulk semiconductors near the band gap, when a large carrier density is present.
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Christian Tanguy (1999) studied this question.
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