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Use of the Bethe Equation for Inner-Shell Ionization by Electron Impact



Cedric J. Powell, Xavier Llovet, Francesc Salvat


We analyzed calculated cross sections for K-, L-, and M-shell ionization by electron impact to determine the energy ranges over which these cross sections are consistent with the Bethe equation for inner-shell ionization. Our analysis was performed with K-shell ionization cross sections for 26 elements, with L-shell ionization cross sections for seven elements, with L3-subshell ionization cross sections for Xe, and with M-shell ionization cross sections for three elements. The validity or otherwise of the Bethe equation could be checked with Fano plots based on a linearized form of the Bethe equation. Our Fano plots revealed two linear regions as predicted by de Heer and Inokuti. For each region, we made linear fits and determined values of the two element-specific Bethe parameters. We found systematic variations of these parameters with atomic number for both the low- and the high-energy linear regions of the Fano plots. We also determined the energy ranges over which the Bethe equation can be used.
Journal of Applied Physics


Bethe equation, Bethe parameters, cross section, electron, inner-shell ionization


Powell, C. , Llovet, X. and Salvat, F. (2016), Use of the Bethe Equation for Inner-Shell Ionization by Electron Impact, Journal of Applied Physics, [online], (Accessed July 21, 2024)


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Created May 13, 2016, Updated June 2, 2021