Using analytic expressions for core and excited-state electron wave functions, we examine the validity of the ‘‘dipole approximation’’ in electron-energy-loss spectroscopy (EELS) due to the L-shell excitations of atoms up to an atomic number of about 50. We derive analytic expressions for the limiting magnitude ${\mathit{q}}_{\mathit{d}}$ of the momentum transfer vector and compare them with expressions for the most likely value of q for a range of chemical elements. We conclude that, although the dipole approximation is good for all L edges for the high incident primary energies typical of transmission EELS, it is of doubtful validity for the ${\mathit{L}}_{\mathrm{II}\mathrm{-}\mathrm{III}}$ edges of the heavier elements for the relatively low primary energies used to increase surface sensitivity in reflection EELS.

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