Modification of the endohedral potential after instant ionization of an inner atom

We investigate here the variation of endohedral A@C$_N$ potential due to instant ionization of an inner atom A. Using a reasonable model to describe the fullerenes shell, we managed to calculate this variation that is a consequence of the monopole polarization of C$_N$ shell. We demonstrate that the phenomenological potentials that properly simulate the C$_N$ shell should belong to a family of potentials with a non-flat bottom, instead of very often used square well potential. As concrete example, we use the Lorentz-bubble model potential. By varying the shape of this potential, we describe the various degrees of the monopole polarization of the C$_N$ shell by positive electric charge at the center of the shell. We calculated the photoionization cross sections of He, Ar, and Xe atoms located at the center of C$_{60}$ shell with and without taking into account accompanying this process monopole polarization of the fullerenes shell. Unexpectedly, we found that the monopole polarization do not affect the photoionization cross sections of these endohedral atoms, thus presenting a very seldom example of potential conspiracy.