A Semi-Empirical, Formula for the Total K-Shell Ionization Cross Section by Electron Impact

The evaluation of some 600 measurements of electron induced K-shell ionization cross sections for elements with 6 ≤ Z ≤ 92 and impact energies of IK ≤ E0 ≤ 5 GeV yielded a set of reliable data, which were used for the derivation of a semi-empirical formula, that enables the prediction of σK for al1 elements and electron bombarding energies. Based on the two-parameter Bethe formula a three-parameter formula was was derived, which depends on β and Z and the three Z-dependent constants. They are needed to describe properly position, slope and height of the cross section maximum as well as the energy behaviour. They were deduced by fitting the three-parameter formula to the evaluated data of eleven elements. Since the constants exhibit a Z dependence, a power law or polynomials were fitted to these quantities. The newly derived formula predicts the the electron induced K-shell ionization cross section for all Z and impact energies to about ± 13%.