Point-ion approximation within the March model for the fullerene molecule

We present an approach of the March model [N. H. March, Proc. Cambridge Philos. Sec. 48, 665 (1952)] for the fullerene molecule by employing a point-ion approximation. Accordingly, the model with which we shall be concerned is a high-density gas of pi electrons in its ground state with a discrete positively charged background disposed in a t - icosahedral symmetry. The density of pi electrons is derived within the first-order approximation of the perturbation theory and then Poisson's equation is solved analytically by imposing natural limits for the fullerene molecule. We have found both inside and outside the fullerene cage distinctive peaks for the electron distribution and a larger fraction of the pi electrons contained inside the molecule. We must stress here that the other results recorded in a continuum positive charge approximation of the March model for the fullerene molecule predict that only less than half of all the pi electrons are inside the shell.