Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T07:49:26.761Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Applications and Implications of Duane's Quantum Theory of Diffraction

Published online by Cambridge University Press:  24 October 2008

E. J. Williams
E. J. Williams
Affiliation:
1851 Exhibition Senior Research Student, Gonville and Caius College
Get access Rights & Permissions [Opens in a new window]

Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 24 , Issue 2 , April 1928 , pp. 343 - 356
Copyright
Copyright © Cambridge Philosophical Society 1928

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

* Proc. Nat. Ac. Sci., 9, 159 (1923).Google Scholar

† Epstein and Ehrenfrest (Proc. Nat. Ac. Sci., 10, 133 (1924)) have shown that these restrictions satisfy the condition of being independent of the arbitrarily chosen axes, and that if a be the spacing in any direction the momentum p in this direction obeys the law p = n(h/a).CrossRefGoogle Scholar

* Proc. Nat. Ac. Sci., 9, 359 (1923).CrossRefGoogle Scholar

† Old quantum theory.Google Scholar

‡ Proc. Nat. Ac. Sci., 10, 133 (1924).CrossRefGoogle Scholar

§ Proc. Nat. Ac. Sci., 9, 238 (1923).CrossRefGoogle Scholar

‖ 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

* If m 0 is the rest mass m=m 0 (1 − v 2/c 2)−1/2.Google Scholar

† Proc. Roy. Soc., 02, 1928.Google Scholar

‡ 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

§ Proc. Nat. Ac. Sci., 13, 518 (1927).CrossRefGoogle Scholar

* Recent experiments by Gray, and Cave, (Proc. Roy. Soc. of Can. 21, 157 (1927)) show that there is considerable excess forward scattering of radiation by a gas due to interference between the radiations scattered by the electrons belonging to the same molecule. The corresponding effect for photoelectrons may, in terms of the wave-mechanics, be described as interference between the ‘ψ’ waves which represent the photoelectron beams from the atom. Most of the photoelectrons produced by X-rays traversing light elements come from the ‘k’ levels in the atoms and the problem is that of the phase relationships between the ‘ψ’ waves due to the separate k electrons.Google Scholar

† Nature, 01. 28, 1928.Google Scholar

‡ Proc. Nat. Ac. Sci., 9, 159 (1923).Google Scholar

* Proc. Nat. Ac. Sci., 12, 140 (1926);CrossRefGoogle Scholar Allison, ibid., 12, 143 (1926).

† A similar result applies to the reflexion of electrons by crystals. Since the mass of a crystal is large compared with the mass of an electron it follows that reflected electrons lose very little energy when they are reflected and as far as loss of energy due to reflexion is concerned reflected electrons must be ‘full-speed’ electrons.Google Scholar

* Phil. Mag., 2, 657 (1926).CrossRefGoogle Scholar

† Nature, 10 15, 1927.Google Scholar

‡ Proc. Roy. Soc., 117, 214 (1927).CrossRefGoogle Scholar

§ Proc. Roy. Soc., 118, 334 (1928).CrossRefGoogle Scholar

* Waller, , Nature, 655, 07 30, 1927;Google ScholarWentzel, , Zeit. für Physik, 43, 779 (1927).CrossRefGoogle Scholar

† Phys. Rev., 25, 314 and 723 (1925).CrossRefGoogle Scholar

* James, , Phil. Mag., 49, 585 (1925);CrossRefGoogle ScholarJames, and MissFirth, , Proc. Roy. Soc., 117, 62 (1927).CrossRefGoogle Scholar

* Physical Optics, p. 429.Google Scholar