  We calculate the radiative lifetime and energy bandstructure of excitons in
semiconducting carbon nanotubes, within a tight-binding approach. In the limit
of rapid interband thermalization, the radiative decay rate is maximized at
intermediate temperatures, decreasing at low temperature because the
lowest-energy excitons are optically forbidden. The intrinsic phonons cannot
scatter excitons between optically active and forbidden bands, so
sample-dependent extrinsic effects that break the symmetries can play a central
role. We calculate the diameter-dependent energy splittings between singlet and
triplet excitons of different symmetries, and the resulting dependence of
radiative lifetime on temperature and tube diameter.
