Energies of higher optical transitions in semiconductor carbon nanotubes

We show that short-range electron interactions in semiconductor carbon nanotubes promote inter-subband coupling. This coupling is revealed in a significant alteration of energies of E$_{33}$ and E$_{44}$ optical transitions with respect to the predictions of the non-interacting model. The influence of the short-range electron interactions is traced analytically and numerically, by switching it off entirely or partly while calculating optical absorption spectra.