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

We review the basic scattering theory for electron impact excitation of single atoms in the scanning transmission electron microscope (STEM). We calculate inelastic images of single atoms for excitations of lithium and compare the results obtained with and without the dipole approximation. We show that the validity of the dipole approximation depends on the form of the target wavefunctions as well as on the size of q·r. For a 100 keV STEM, we show that the dipole approximation should not be used when the energy loss is less than about 50 eV.