  The existence of a system of short-live discrete volume-localized electron
quantum levels in positively charged fullerenes is theoretically and
numerically demonstrated using the example of fullerenes C60 and C20. Unlike
well-studied experimentally and theoretically electron states localized in a
thin surface layer, these electron states are due to the flat part of the
Coulomb potential of a positively charged fullerene sphere. The energy width of
the system of such discrete volume-localized levels depends on the charge and
increases with charge increasing. For C60+1, the energy width is 0.32 a.u. and
increases up to 1.9 a.u. for fullerene C60+10. Thus, the electrons captured on
these discrete levels of fullerene form a sort of a short-lived "nano-atom" or
"nano-ion", in which the electrons are localized inside a positively charged
spherical "nucleus". Numerous published papers have demonstrated theoretically
and experimentally the existence of metastable positively charged C60
fullerenes with a charge of +10 or more, which suggests the possibility of
experimental observation of the considering system of volume-localized
electronic states.
