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Physical Review

Simultaneity in the Compton Effect

R. Hofstadter, John A. Mcintyre

Published Apr 1, 1950• 20 citations
Publisher

Abstract

The Bothe-Geiger experiment has been repeated under improved conditions of time resolution, obtained by using stillbene scintillation counters. The recoil electron and scattered photon are emitted together within a time interval of less than 1.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ second. The electron and photon are also projected without a delay larger than 1.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ second after arrival of a quantum. The familiar concepts used in discussions of the Compton effect are shown to be valid.

DOI
10.1103/physrev.78.24

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The Bothe-Geiger experiment has been repeated under improved conditions of time resolution, obtained by using stillbene scintillation counters. The recoil electron and scattered photon are emitted together within a time interval of less than 1.5\ifmmode\times\else\texttimes\fi{}10\ensuremath−8{10}^{\ensuremath{-}8}10\ensuremath−8 second. The electron and photon are also projected without a delay larger than 1.5\ifmmode\times\else\texttimes\fi{}10\ensuremath−8{10}^{\ensuremath{-}8}10\ensuremath−8 second after arrival of a quantum. The familiar concepts used in discussions of the Compton effect are shown to be valid.
The simultaneity in the Compton effect has been investigated by using scintillation counters and fast coincidence techniques. By the use of a gamma-ray source of a known, very short, lifetime (Ni60{\mathrm{Ni}}^{60}Ni60) it was possible to apply a first moment investigation to the time delays involved.It is shown that the order of magnitude of all possible time delays involved in the Compton effect does not exceed ${10}^{\ensuremath{-}11}$ second. Upper limits previously given were \ensuremath{\sim}${10}^{\ensuremath{-}8}$ second.
A test has been made of the photon theory of the scattering of high frequency radiation. The pairs of scattered photons and recoil electrons predicted by this theory have been looked for by means of specially designed Geiger-M\"uller counters. Coincident discharges in the electron and photon counters were recorded by means of a vacuum tube amplifying and adding circuit. The scatterers used were air, aluminum, beryllium, filter paper and paraffin. The radiation was the gamma-rays from radium C. Experiments were performed with the counters set at various angles, some where the photon theory predicts coincidences, and others where coincidences should not be expected. The experiments uniformly gave fewer coincidences in the correct positions than were expected, and those observed could in every case be accounted for as chance coincidences due to the finite resolving time of the apparatus. It has not been found possible to bring the results of these experiments into accord with the photon theory of scattering. The wave-mechanical theory of the scattering process has not yet been extended to include the gamma-ray region so that it is impossible to compare this theory with the present experiments. Unless it is shown that the two theories disagree in the gamma-ray region it does not seem possible to reconcile the present experiment with the Bothe-Geiger and Compton-Simon experiments.
The Compton equation is normally developed using the photon model, but it is also capable of derivation based on a classical wave model of light, and there is a considerable history of such derivations, including one by Compton himself. A simple derivation in the laboratory frame based on waves scattered by a statistical aggregate of recoil electrons is developed in this paper, providing a bridge between microscopic events and macroscopic observation, and implications of coexisting wave and particle model derivations of the Compton effect are discussed. The parallel derivations based on contrasting models can also furnish an instructive exercise for students.
Compton scattering figures prominently in the introductory chapters of textbooks on quantum mechanics as providing evidence for the ‘‘particulate’’ nature of light. It also arises in discussions of ‘‘Heisenberg’s microscope,’’ in which it is shown that attempts to measure the position and the momentum of an electron simultaneously are governed by the uncertainty principle. However, recent developments in Compton scattering have not yet found their way into the textbooks. In this paper we review the history of the Compton effect and describe briefly some of the modern developments in x-ray and electron Compton scattering and their application to the study of electron momentum densities which we believe to have a pedagogical value. Finally, we return to Heisenberg’s microscope, and show how it has now become a reality. A complete analysis for all scattering angles depends crucially on the different expressions for the resolution and the depth of focus of the microscope.