  Theoretical expressions for ionization cross sections by electron impact
based on the binary encounter Bethe (BEB) model, valid from ionization
threshold up to relativistic energies, are proposed. The new modified BEB
(MBEB) and its relativistic counterpart (MRBEB) expressions are simpler than
the BEB (nonrelativistic and relativistic) expressions because they require
only one atomic parameter, namely the binding energy of the electrons to be
ionized, and use only one scaling term for the ionization of all sub-shells.
The new models are used to calculate the K-, L- and M-shell ionization cross
sections by electron impact for several atoms with Z from 6 to 83. Comparisons
with all, to the best of our knowledge, available experimental data show that
this model is as good or better than other models, with less complexity.
