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Published online by Cambridge University Press: 24 October 2008
Duane's quantum theory of diffraction is applied to the reflexion of electrons by crystals and to the spatial distribution of photoelectrons and fluorescent radiation from a crystal.
Two alternative criteria for coherence are given. According to the second of these there is coherence provided that the momentum imparted to the components of a system during the process concerned is insufficient, owing to quantum restrictions to their motion, to change their energy. Calculations made on this supposition show that in the case of the scattering of radiation by a crystal there is complete coherence for the lower orders, while for higher orders this ceases to be the case and the reflected intensity is reduced as the result of incoherent scattering. The specular reflexion by gases is also considered.
Duane's theory of diffraction has not been placed on a rigorous basis and the solutions which have been proposed here for various problems may be incorrect. Even so the theory has at least served to bring to light several points of theoretical and experimental interest which deserve consideration.
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‖ In applying the correspondence principle the stationary states before and after a transition are taken into account, so that the intensities according to the Epstein-Ehrenfrest calculations are not absolutely identical with the classical intensities which are obtained by applying classical theory to the initial state only. In the case of reflexion by a crystal the difference is small because the change in velocity of a crystal corresponding to a change in its momentum of the order of h/a is small. If the scattering system be light and consist say of only one electron the difference between the two theories is appreciable. The application of the quantum theory and the correspondence principle to this case has been made by Breit, (Phys. Rev., 27, 362 (1926)) and experiment decides in its favour, the Compton effect and departure from Thomson scattering being unintelligible on the classical theory.CrossRefGoogle Scholar
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‡ Davisson, and Germer, (Phys. Rev., 30, 705 (1927)) have made experiments with much slower electrons than those used by Thomson, and surface potential effects and the considerable absorption of the electrons in traversing the crystal lead to complications. Davisson and Germer interpret some of their “reflexions’ as the result of diffraction from a single layer of atoms at the surface of the crystal. The quantum theory of diffraction allows this only if the top layer alone acts as a whole in scattering the electron beam concerned.CrossRefGoogle Scholar
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