Relativistic effects in atomic inner-shell ionization by a focused electron probe

A relativistic theory of atomic inner-shell ionization is presented in a form directly applicable to the calculation of the electron energy loss signal obtained using a focused electron probe in a scanning transmission electron microscope. Expressions are given for the implementation of the theory assuming a central potential atomic model. Analytical and numerical calculations are used to demonstrate that, for points in the diffraction plane lying close to the optic axis, the difference between the relativistic and nonrelativistic theories can be significant, even for an incident energy of 100 keV (usually considered too low an energy for relativistic effects to be important). Implications for the quantitative matching of experimental and simulated data are discussed.