On The Low-Frequency Vibrational Modes of C$_{60}$

The vibrational spectrum of C$_{60}$ is compared to the spectrum of a classical isotropic elastic spherical shell. We show correlations between the low frequency modes of C$_{60}$ and those of the spherical shell. We find the spherical model gives the approximate frequency ordering for the low frequency modes. We estimate a Poisson ratio of $\sigma\approx 0.30$ and a transverse speed of sound of $v_s\approx 1800$ m/s for the equivalent elastic shell. We also find that $\omega({\rm M_1})/\omega({\rm M_0})=\sqrt{3\over 2}$ for the shell modes ${\rm M_0}$ and ${\rm M_1}$, independent of elastic constants. We find that this ratio compares favorably with an experimental value of 1.17.