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Exciton energy levels and corresponding optical spectra are calculated in carbon nanotubes (CN) in the conventional screened Hartree-Fock approximation within a k · p scheme. The Coulomb interaction gives rise to several exciton bound states as well as the increase of the energy gap. The exciton energy is shifted to higher energy side than the unperturbed band gap because the effect on the band gap is larger. The considerable amount of the optical intensity is transferred to exciton bound states because of the one-dimensional nature of CN's.
Tsuneya Ando (Tue,) studied this question.