Cross sections for ionization of inner-shell electrons by electrons

A survey is given of the available cross-section data for ionization of inner-shell electrons by incident electrons in the range of interest for electron-probe microanalysis and for Auger-electron spectroscopy of solid surfaces. Owing to the paucity of data, the bulk of the discussion is limited to $K$-shell and $L$-shell ionization of light atoms. Calculated, semiempirical, and experimental cross-section data have been intercompared graphically and through fits to the linearized Bethe equation for inner-shell ionization (the Fano plot). Almost all of the data could be satisfactorily fitted over the range $4\lesssim U_{\mathrm{nl}}\lesssim 30$, where $U_{\mathrm{nl}}=\frac{E_0}{E_{\mathrm{nl}}}$, $E_0$ is the incident electron energy, and $E_{\mathrm{nl}}$ the binding energy of electrons in the $\mathrm{nl}$ shell. From these fits, values could be obtained of the "effective" Bethe parameters $b_{\mathrm{nl}}$ and $c_{\mathrm{nl}}$. Values of the parameter $b_{\mathrm{nl}}$ have also been derived from photoabsorption data and were found to be generally consistent with the ionization data if account was taken of the distribution of differential oscillator strength with respect to excitation energy and the consequent expected variation of $b_{\mathrm{nl}}$ with incident electron energy. The derived "effective" Bethe parameters should not therefore be used outside the range of each fit.