  The optical absorption spectrum of the carbon (4,2) nanotube is computed
using an ab-initio many-body approach which takes into account excitonic
effects. We develop a new method involving a local basis set which is symmetric
with respect to the screw symmetry of the tube. Such a method has the
advantages of scaling faster than plane-wave methods and allowing for a precise
determination of the symmetry character of the single particle states,
two-particle excitations, and selection rules. The binding energy of the
lowest, optically active states is approximately 0.8 eV. The corresponding
exciton wavefunctions are delocalized along the circumference of the tube and
localized in the direction of the tube axis.
