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Journal of Physics B Atomic Molecular and Optical Physics

Wave–particle duality of radiation in Compton scattering

Krunoslav Pisk, Zoran Kaliman, Nataša Erceg

Published Nov 18, 2016• 10 citations
Publisher

Abstract

Abstract In this work we analyze the wave–particle aspects of radiation in (incoherent) Compton scattering in the radiation energy range from 2–100 keV. From the calculated cross sections of the scattering from the electron (positron), hydrogen and positronium we construct the interpretation functions (IFs), where our assertion is that the Compton scattering from the free electron (positron) is an established example of the particle behavior of radiation. These IFs estimate the possibility of the interpretation of radiation in terms of waves or particles in an analogy with the analysis carried out in the coherent scattering of light. Based on these IFs we propose a new criterion for the estimation of the validity of the impulse approximation (IA).

DOI
10.1088/0953-4075/49/23/235004

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Abstract In this work we analyze the wave–particle aspects of radiation in (incoherent) Compton scattering in the radiation energy range from 2–100 keV. From the calculated cross sections of the scattering from the electron (positron), hydrogen and positronium we construct the interpretation functions (IFs), where our assertion is that the Compton scattering from the free electron (positron) is an established example of the particle behavior of radiation. These IFs estimate the possibility of the interpretation of radiation in terms of waves or particles in an analogy with the analysis carried out in the coherent scattering of light. Based on these IFs we propose a new criterion for the estimation of the validity of the impulse approximation (IA).
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.
The Compton effect is commonly cited as a demonstration of the particle feature of light, while the wave nature of matter has been proposed by de Broglie and demonstrated by Davisson and Germer with the Bragg diffraction of electron beams. In this investigation, we present an entirely different interpretation of the Compton effect based on the postulates of de Broglie and on an interaction between electromagnetic and matter waves. The speeds of interacting electrons in the Compton scattering are quite fast and its mechanism relies heavily on the mass variation. Thus, based on this wave interpretation, the Compton effect can be viewed as a further demonstration of the postulates of de Broglie for high-speed particles. In addition to the scattered wave, a direct radiation depending on the mass variation is predicted, which provides a means to test the wave interpretation.
Scattering of a plane electromagnetic wave by free and bound wave packets is analyzed by semiclassical radiation theory. It is shown that the theory gives the correct answer to the question of radiation intensity in the photoelectric effect and to the correlation problem in Compton scattering. The expression for the intensity of the scattered radiation differs from the cross section which is derived from the model based on the particle nature of the electromagnetic field. The meaning of this difference is discussed. Low frequency spectrum of the scattered radiation on a bound charge is obtained.
The reduction of a particle's wave function in the process of radiation or light scattering is a longstanding problem.Its solution will give a clue on processes that form, for example, wave functions of electrons constantly emitting synchrotron radiation quanta in storage rings.On a more global scale, it may shed light on wave function collapse due to the process of measurement.In this paper we consider various experimental options using Fermilab electron beams and a possible electron beam from the SNS linac and lasers to detect electron wave function change due to Compton scattering.
We calculate the differential cross sections for Compton scattering of photons described by Hermite Gaussian (HG) wave function in the framework of relativistic quantum mechanics. The HG wave gamma-rays propagating along the z-direction have quantum numbers of nodes of nx and ny in the x- and y-directions, respectively. The calculated differential cross section is symmetric with respect to both the zx- and zy-planes. The nodes whose number is identical with nx and ny appear in the energy spectrum measured in zx- and zy-planes, respectively. These results indicate that it is possible to identify the HG wave photon and its quantum numbers nx and ny by measuring Compton scattering. The present proposed method can be also applied to gamma-ray astronomy.
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.