  The properties of excitons in semiconducting single-walled carbon nanotubes
(SWCNTs), isolated in vacuum or a medium, and their contributions to the
optical spectra of nanotubes are studied within the elementary potential model,
in which an exciton is represented as a bound state of two oppositely charged
quasi-particles confined to the nanotube surface. The emphasis is given on the
influence of dielectric environment surrounding a nanotube on the exciton
spectra. For nanotubes in environment with permittivity less than 1.8 the
ground-state exciton binding energies exceed the respective energy gaps, while
the obtained binding energies of excitons in nanotubes in a medium with
permittivity greater than 4 are in good accordance with the corresponding
experimental data and consistent with known scaling relation for the
environmental effect. The stabilization process of single-electron spectrum in
SWCNTs in media with rather low permittivities is discussed.
