title: Use of the Bethe Equation for Inner-Shell Ionization by Electron Impact.
abstract: 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, which display theoretical cross sections and available measured cross sections, reveal 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.
authors.affiliation: Materials Measurement Science Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8370, USA.
authors.forename: Cedric J
authors.initials: CJ
authors.lastname: Powell
authors.affiliation: Centres Científics i Tecnològics, Universitat de Barcelona, Lluís Solé i Sabarís 1-3, 08028 Barcelona, Spain.
authors.forename: Xavier
authors.initials: X
authors.lastname: Llovet
authors.affiliation: Facultat de Física (ECM and ICC), Universitat de Barcelona, Diagonal 645, 08028 Barcelona, Spain.
authors.forename: Francesc
authors.initials: F
authors.lastname: Salvat