  We present a comprehensive study of the chiral-index assignment of carbon
nanotubes in aqueous suspensions by resonant Raman scattering of the radial
breathing mode. We determine the energies of the first optical transition in
metallic tubes and of the second optical transition in semiconducting tubes for
more than 50 chiral indices. The assignment is unique and does not depend on
empirical parameters. The systematics of the so-called branches in the Kataura
plot are discussed; many properties of the tubes are similar for members of the
same branch. We show how the radial breathing modes observed in a single Raman
spectrum can be easily assigned based on these systematics. In addition,
empirical fits provide the energies and radial breathing modes for all metallic
and semiconducting nanotubes with diameters between 0.6 and 1.5 nm. We discuss
the relation between the frequency of the radial breathing mode and tube
diameter. Finally, from the Raman intensities we obtain information on the
electron-phonon coupling.
