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Theoretical expressions for ionization cross sections by electron impactbased on the binary encounter Bethe (BEB) model, valid from ionizationthreshold up to relativistic energies, are proposed. The new modified BEB(MBEB) and its relativistic counterpart (MRBEB) expressions are simpler thanthe BEB (nonrelativistic and relativistic) expressions because they requireonly one atomic parameter, namely the binding energy of the electrons to beionized, 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 crosssections by electron impact for several atoms with Z from 6 to 83. Comparisonswith all, to the best of our knowledge, available experimental data show thatthis model is as good or better than other models, with less complexity.

Modified binary encounter Bethe model for electron-impact ionization