Theory and it ab initio calculation of radiative lifetime of excitons in   semiconducting carbon nanotubes
  We present theoretical analysis and first-principles calculation of the radiative lifetime of excitons in semiconducting carbon nanotubes. An intrinsic lifetime of the order of 10 ps is computed for the lowest optically active bright excitons. The intrinsic lifetime is however a rapid increasing function of the exciton momentum. Moreover, the electronic structure of the nanotubes dictates the existence of dark excitons nearby in energy to each bright exciton. Both effects strongly influence measured lifetime. Assuming a thermal occupation of bright and dark exciton bands, we find an effective lifetime of the order of 10 ns at room temperature, in good accord with recent experiments. 
Catalin D. Spataru, Sohrab Ismail-Beigi, Rodrigo B. Capaz, and Steven   G. Louie