Distribution of spectral moments for the radial breathing mode of single wall carbon nanotubes

Raman scattering of the radial breathing mode of single wall carbon nanotubes was measured with a large number of different laser lines. The first and the second moments of the spectral distribution were evaluated for all recorded spectra and were found to exhibit damped oscillations with the excitation energy. The oscillations originate from the confinement of the electrons into states distributed within the van Hove singularities. An extended as well as an approximate calculation of the moments yields very good agreement with the experiments and allows to determine the diameter of the nanotube bundles. Using the approximate calculation the mean diameter and the width of the diameter distribution can be evaluated from a single Raman experiment.