  A mass and spring model is used to calculate the phonon mode dispersion for
single wall carbon nanotubes (SWNTs) of arbitrary chirality. The calculated
dispersions are used to determine the chirality dependence of the radial
breathing phonon mode (RBM) density. Van Hove singularities, usually discussed
in the context of the single particle electronic excitation spectrum, are found
in the RBM density of states with distinct qualitative differences for zig zag,
armchair and chiral SWNTs. The influence the phonon mode density has on the two
phonon resonant Raman scattering cross-section is discussed.
