The analysis of the Raman scattering cross section of the radial breathing modes of double-wall carbon nanotubes allowed us to determine the optical transitions of the inner tubes. The Raman lines are found to cluster into species with similar resonance behavior. The lowest components of the clusters correspond well to sodium sodecyl sulfate wrapped high pressure carbon monoxide grown tubes. Each cluster represents one particular inner tube inside different outer tubes and each member of the clusters represents one well-defined pair of inner and outer tubes. The number of components in one cluster increases with the decreasing inner tube diameter and can be as high as 14 spread over $30{\mathrm{cm}}^{-1}$. This suggests a lot of variation in the diameter difference of inner-outer tube pairs.

• Received 19 August 2005

DOI:https://doi.org/10.1103/PhysRevB.72.161404