Specific properties of Hartree-Fock equations due to exchange and non-linearity are considered. Particular attention is given to an atom in a strong electric static field. It is demonstrated that exchange between outer and inner electrons, taken into account by the so-called Fock term affects strongly the long-range behavior of the inner electron wave function. As a result, it dramatically increases its probability to be ionized.
A simple model is analyzed demonstrating that the decay probability,
compared to the case of a local (Hartree) atomic potential, increases by
many orders of magnitude. As a result of such increase, the ratio of
inner to outer electrons ionization probability became not too small.
It is essential that the effect of exchange upon probability of inner
electron ionization by strong electric field is proportional to the
square of the number of outer electrons. It signals that in clusters of
fullerenes the inner electron ionization by strong field, the very fact
of which is manifested by e.g. high energy quanta emission, has to be
essentially increased as compared to this process in gaseous atomic