Behavior of the ionization cross sections at high incident electron en
ergies E >> I was considered, where I is the binding energy of the tar
get. Presenting the total ionization cross section as a sum of the cla
ssical and dipole (Bethe), terms the dependences of the ionization cro
ss sections on the principal and orbital quantum numbers of the target
are investigated. The applicability of the asymptotic formulas obtain
ed is discussed on the basis of comparison with ionization cross secti
ons calculated in the Born approximation for high n states.