Monopole polarization of C60 fullerene shell by an electric charge in its center

The spatial distributions of electric charges forming the C60 shell have been analyzed with the Poisson equation. It has been shown that the modification of formulas for the rectangular-potential-well as a model potential of the C60 shell by means of addition to them the Coulomb-potential-like terms does not describe the monopole polarization of the shell by the electric charge Z in the center of the shell. The phenomenological potentials simulating the C60 shell potential should belong to a family of potentials with a non-flat bottom. In the paper some model potentials have been proposed and discussed. It has been shown that by varying the semithiknesses of these potential wells we could describe the various degrees of the monopole polarization of the C60 shell that due to shifting of collectivized electrons of the shell relative to the rigid positive carcass of C60 fullerene. Constructed here, the model potentials for the C60 shell can be used to describe the processes of elastic electron scattering by endohedral A+@C60 positive ions.