Corrections to the Incoherent Scattering Factors for Electrons and X Rays

Abstract

The usual use of the closure relation in the derivation of the incoherent scattering factor for electrons and x rays involves approximations and introduces errors in the final result. In this paper corrections through third order for these errors are given. The correction terms are found to be of a simple form and can be quite important not only in the limit of low energy for the incident electron or x‐ray beam but also for atoms of large atomic number. The magnitudes of the corrections for Ne and Ge are given for 40‐kV electrons. In the x‐ray case corrections are given for Ge for Cu Kα x radiation.