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Use of the Bethe equation for inner-shell ionization by electron impact
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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, L-3-subshell ionization cross sections for Xe, and 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, which display theoretical cross sections and available measured cross sections, reveal two linear regions as predicted by de Heer and Inokuti [in Electron Impact Ionization, edited by T. D. Mark and G. H. Dunn, (Springer-Verlag, Vienna, 1985), Chap. 7, pp. 232-276]. 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.
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POWELL, Cedric j., LLOVET XIMENES, Xavier, SALVAT GAVALDÀ, Francesc. Use of the Bethe equation for inner-shell ionization by electron impact. _Journal of Applied Physics_. 2016. Vol. 119, núm. 18, pàgs. 184904. [consulta: 7 de febrer de 2026]. ISSN: 0021-8979. [Disponible a: https://hdl.handle.net/2445/127902]