  We develop a theory of inter-valley Coulomb scattering in semiconducting
carbon-nanotube quantum dots, taking into account the effects of curvature and
chirality. Starting from the effective-mass description of single-particle
states, we study the two-electron system by fully including Coulomb
interaction, spin-orbit coupling, and short-range disorder. We find that the
energy level splittings associated with inter-valley scattering are nearly
independent of the chiral angle and, while smaller than those due to spin-orbit
interaction, large enough to be measurable.
