Limitations of the dipole approximation in calculations for the scanning transmission electron microscope

We review the basic scattering theory for electron impact excitation of sin gle atoms in the scanning transmission electron microscope (STEM). We calcu late inelastic images of single atoms for excitations of lithium and compar e the results obtained with and without the dipole approximation. We show t hat the validity of the dipole approximation depends on the form of the tar get wavefunctions as well, as on the size of q.r. For a 100 keV STEM, we sh ow that the dipole approximation should not be used when the energy loss is less than about 50 eV. (C) 1999 Elsevier Science B.V. All rights reserved.