On the possibility of considering the fullerene shell C60 as a conducting sphere

It has been shown that the fullerene shell in the static electric field behaves as a set of separate carbon atoms, rather than a conducting sphere [1]. We calculate the effective electric field ${\rm {\bf E}}_{eff} (\omega )$ at the fullerene center when the external ${\rm {\bf E}}(\omega )$ with frequency $\omega $ is applied to C$_{60}$. The modification of the external field comes from the effect of the dynamic dipole polarizability $\alpha _d (\omega )$ of the fullerene C$_{60}$ expressed via its total photoionization cross-section $\sigma (\omega )$[2]. We calculate the ratio $\eta (\omega )\equiv {\rm {\bf E}}_{eff} (\omega )/{\rm {\bf E}}(\omega )$ and then investigate whether $\eta (0)$ is equal to zero. The equality of the ratio $\eta (\omega )$ to zero in the static limit $\omega \to 0$ is the critical condition being general for a conducting body with any form. For C$_{60}$ this ratio is$\eta (0)\approx 2$, i.e. C$_{60}$ is not a hollow metallic sphere. It is shown that at any $\omega $ the frequency dependence of the ratio of the fields $\eta (\omega )$ at the center of the C$_{60}$ molecule and outside it has nothing to do with $\eta (\omega )$for the conducting sphere [1], which is additional evidence that the C$_{60}$ shell is strongly non-metallic. [1] J.-P. Connerade and A. V. Solov'yov, J. Phys. B 38, 807 (2005) [2] J. Berkowitz, J. Chem. Phys. 111, 1446 (1999).