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Physical Review

An Apparent Failure of the Photon Theory of Scattering

Robert S. Shankland

Published Jan 1, 1936• 38 citations
Publisher

Abstract

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.

DOI
10.1103/physrev.49.8

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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 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.
Chapter I The origins of quantum physics I The Compton effect — a strange dichotomy in the nature of electromagnetic radiation In a series of experiments conducted between 1919 and 1923, Arthur Holly Compton (Figure 1.1) investigated the scattering of monochromatic (single-wavelength) X-rays from graphite targets. He found that the radiation scattered at an angle 0 to the incident beam contained, in addition to radiation of the same wavelength as the incident radiation, a second component with a considerably longer wavelength. The existence of this second component in the scattered radiation could not be explained by the well-established theory of the scattering of electromagnetic waves by electrons. Compton considered instead the process illustrated in Figure 1.2, in which a particle of electromagnetic radiation, collides with a slow moving electron, which then recoils absorbing some of the X-ray particle’s energy. Treating the process as a collision between particles, and using only the (relativistic) conservation laws of energy and momentum, Compton was able to account for the effect completely. However, at the same time, in the same experiment, Compton was using interference effects, depending wholly on the wave model, in order to determine the wavelength of the scattered radiation. So here was an experiment which apparently required the simultaneous use of both the wave and particle models of electromagnetic radiation for the interpretation of the results! The existence of this strange dichotomy in the nature of electromagnetic radiation was just one indication of the need for a radical revision of views regarding the physical world.
A study has been made of the X-rays symmetrically diffracted by the (130) and (10) planes of NaCl. The object of the study was to determine whether or not X-rays are diffracted in both directions simultaneously. Two Geiger Muller counters were used to detect the X-rays. A coincidence circuit was connected to the two counters. Over 20 million quanta were counted by each counter, yet only 12 thousand apparent coincidences were observed. A detailed study of the data reveals that this small number of coincidences is best interpreted by assuming no coherence between the two diffracted X-ray beams and attributing the coincidence counts to the chance arrival of two quanta, one at each counter, separated in time by less than the resolving time of the coincidence circuit. This lack of coincidence is in accord with the quantum picture of radiation.
The Compton scattering is an elastic collision of the x-ray or gamma photons with free electrons (or loosely bound valence shell electrons). This scattering is demonstrated in Fig. 1. In this communication we are combining Heisenberg's uncertainty principle and the Compton scattering. Note, that some of the expressions (including their derivations) of this communication can be found in modern physics textbooks. Figure 1. Schematic representation of Compton scattering, in which an incoming photon scatters from an electron at rest. The electron of the rest mass m e has the rest energy of E r = m e c 2. The Compton scattered electron (hereinafter the Compton electron) posses a relativistic kinetic energy, the relativistic speed υ e and the linear momentum p e = m e υ e. Before scattering, let the photon moves along the positive x-axis having an energy E 0 = hν 0 , frequency ν 0 , wavelength λ 0 and linear momentum p 0 = hν 0 /c, where h (= 6.63 × 10-34 J s) is the Planck constant and c (= 2.99792×10 8 m s-1) is the speed of light. After scattering, the photon moves at an angle θ off the x-axis with an energy E = hν, frequency ν, wavelength λ and momentum p = hν/c. The conservation of linear momentum of the electron after the collision yields, p e 2 = p 0 2 + p 2-2p 0 pcosθ.
The undergraduate courses on modern physics generally consider the particle interpretation of Compton effect. Motivated by a student's solution in an undergraduate examination on modern physics here we consider the wave characteristics of recoiled electrons in the Compton effect. The de Broglie wavelength, wave and clock frequency of the scattered electrons are expressed in terms of the wavelength and the frequency of the incident and the scattered photons respectively using the familiar particle interpretation of the Compton effect, where initially the electron is at rest and its spin is ignored. Both non-relativistic and relativistic cases are considered. Numerical values of de Broglie wavelength, wave and clock frequency of the scattered electron are calculated for an incident photon energy that was used in the original experiment of Compton as a function of the scattering angle of the recoiled electron. Considering the relativistic effects which are however insignificant for the de Broglie wavelength of the recoiled electron under these conditions, the minimum value obtained is in the range of X-rays. The non-relativistic de Broglie wave frequency obtained by neglecting the rest mass of the electron leads to an underestimation of its value. The implications of de Broglie wavelength and clock frequency for Compton scattering experiments are briefly discussed and possible extensions of the obtained mathematical formulations are indicated. The results are useful for understanding the wave-particle duality of the recoiled electron in the context of the Compton effect.