The Born Approximation in Electron Diffraction

Abstract

THE Born approximation for the electron wave scattered by an atom has been universally employed for the interpretation of electron diffraction experiments directed toward the determination of molecular or crystal structure. There is some justification for this. Quantitative measurements of diffraction intensities performed to test the applicability of the approximation for electrons of the energies usually used in structure work have, on the whole, been regarded as satisfactory verifications. In structure work itself—in the work on gas molecules, for example—the considerable success resulting from it use has led to the feeling that even in the presence of heavy atoms there might not be serious error. There has perhaps been the implicit faith that whatever theoretical refinements were lacking would at least not alter substantially the structures to be derived. We have found, however, that there is a phase shift on scattering, not given by the first Born approximation (this is the familiar Born approximation, the first term of a power-series expansion in the parameter α = − Ze²/hv), which is approximately proportional to atomic number, depends on angle of scattering, and may become large and important. The suggestion of the existence of this phase shift arose from the cases of uranium hexafluoride (UF₆) and some other gas molecules.