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Le Journal de Physique Colloques

COHERENT INTERACTIONS OF PHOTONS AND ELECTRONS IN CRYSTALS CLOSE TO THE BRAGG ANGLE

K. Das Gupta

Published Oct 1, 1971• 1 citation
Publisher

Abstract

Introduction.-A few new ideas and results in connection with the coherent interaction processes of X-rays in crystals are presented in this talk.This includes the discussion of interaction processes of X-rays and electrons associated with the interference in crystals.The interference is the simplest phenomenon which establishes a correlation between electrons or photons in crystals and thereby introduces coherence in the final output.In the case of X-rays and electrons the most fundamental interference phenomenon is the Bragg scattering in crystals.This is essentially the interaction of electromagnetic waves in case of X-rays and the de Broglie waves in the case of electrons which are to be scattered by the periodic lattice waves involved in the scattering process.In Ewald's [I] dynamical theory of X-ray interference the scattering elements of the crystal act as vibrating dipoles at the lattice sites and the problem is to find in the crystal a balanced or self-consistent state of electromagnetic field and the dipole waves.In Ewald's [I] dynamical theory explaining the Bragg scattering, the scattered waves have the same angular frequency coo of the incident wave.Slater [2] described the interaction between the inci-

DOI
10.1051/jphyscol:1971462

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Introduction.-A few new ideas and results in connection with the coherent interaction processes of X-rays in crystals are presented in this talk.This includes the discussion of interaction processes of X-rays and electrons associated with the interference in crystals.The interference is the simplest phenomenon which establishes a correlation between electrons or photons in crystals and thereby introduces coherence in the final output.In the case of X-rays and electrons the most fundamental interference phenomenon is the Bragg scattering in crystals.This is essentially the interaction of electromagnetic waves in case of X-rays and the de Broglie waves in the case of electrons which are to be scattered by the periodic lattice waves involved in the scattering process.In Ewald's [I] dynamical theory of X-ray interference the scattering elements of the crystal act as vibrating dipoles at the lattice sites and the problem is to find in the crystal a balanced or self-consistent state of electromagnetic field and the dipole waves.In Ewald's [I] dynamical theory explaining the Bragg scattering, the scattered waves have the same angular frequency coo of the incident wave.Slater [2] described the interaction between the inci-
Since the first experiments of the quantum modulation of electron beams by lasers with a crystal as medium in the interaction area ~d1warz-Hora effect) were reported, extensive theoretical studies were performed.A very detaile/ rLproduction of these experiments was achieved (by Andrick and Langhans, further by Weingartshofer et al) where the medium in the interaction area was a gas.The initial clarification of the experiments with crystal as a quantum phenomenon is using a threshold defining a correspondence principle for electromagnetic interaction.Recent experiments by Weingartshofer et al independently confirm this correspondence principle.For two other experiments the ranges of quantum and classical regimes are elaborated to explain the basically differing character of observations.The discussion of the coherence for matter waves is followed up from the beginning of the Schwarz-Hora effect including developments reviewed by Hawkes and indicating further generalizations by the Hanbury-Brown/ Twiss effect.A consequent generalization of the scattering theory of the quantum modulation is presented based on a Green's function solution which results in the fact that far-field superpositions only lead to interferences.The problems of the re-emission of photons from quantum modulated electron beams is discussed and experiments on indirect observations of the phenomena in microwave amplification and in the 1/f noise Handel effect are reported.In the last case. . the self-interaction of electrons are involved in the Handel effect.A further second-quantised derivation and the coherent state Handel effect is presented.
The X rays Diffraction Experiment covers: theory, interaction of photons with the matter, sources of x rays, x rays tube, radioactivity, x rays detector, x rays diffraction process, crystals, miller indices and Bravais lattices, Bragg reflection on crystal, symmetry elements, point group of symmetry, fourteen bravais lattices, crystalline systems bravais, 32 crystalline punctual groups, stereogram of the 32 crystalline punctual groups, brillouin zone and the cubic system lattice, real space (direct lattices) and the reciprocal space (reciprocal lattices), the Laue experiment of x rays diffraction on crystal, experimental set up, scintillators and photomultipliers.Besides, it is researched the Electron Diffraction and the Diffraction and Interference for the electron by using the Fourier Approach and Wave Properties, Diffraction: Heisenberg's Uncertainty Principle, Uncertainty Principle of Heisenberg by applying wave properties, Interference: Double Slit Experiment, The Copenhagen Interpretation, Pilot wave interpretation and why the electron doesn´t radiate energy as a particle.For other hand, Albert Einstein wrote in a research article: "Does the inertia of a body depend on its energy content?" (Ist die Trägheit eines Körpers von seimen Energienhalt abhängig?):"If a body emits energy E in the form of radiation, its mass decreases by E/c 2 ".The fact that the energy that leaves from the body is converted into radiation energy makes no difference, so the more general conclusion is reached that the mass of a body is a measure of the content of its energy...It is not impossible that with bodies whose content of energy is highly variable (for example radio salts) the theory can be successfully tested.If the theory corresponds to the fact, radiation conducts inertia between the bodies that emit and absorb it 1 ".This is true for any type of radiation emitted (gravitational or electromagnetic energy) which produces a decrease in the mass of the body.Respect to the gravitational energy emission, it is demonstrated by theory, experiment and result the discovery formula which describe exactly the variant mass of a particle which emits gravitational energy which was demonstrated by myself at the article: The Fundament of the Mass and Effects of the Gravitation on a Particle and Light in the mass, time, distance, velocity, frequency, wavelength: Variant Mass for a Particle which emits Gravitational Energy for a particle orbiting a large Planet or Sun and for a Binary Star and Variant Frequency for the Light passing close a Gravitational Field from a Massive Object (Sun).The results of the mass formula are of great relevance for Gravitational Interactions.It is in accordance with the classic result for the emission of the total gravitational energy (bond total energy) for a particle orbiting a large Planet or Sun and for a Binary Star.At the atom, the electron only radiates this energy when it jumps from one orbit to another orbit at the atom.It is in accordance with the experimental results from the spectral lines of the atom.The difference is that in a gravitational field the particle or a planet around the sun can take any position at the space and any radius.But, the electron at the atom only can take restricted positions which are explained by quantum mechanics, and the electrons don´t emit radiation when they orbit around the nucleus.At this article, it is demonstrated the development formula for the variant mass of the electron at the atom which describe exactly the variant mass of the electron (charged particle) at the atom which emits electromagnetic energy from one stationary level to other.The results of the formula are compared with the ionization energy emission for the electron at the atom and the bound energy for the diatomic molecules.The results are in agreement with high accuracy.Besides, Maxwell's theory shows that electromagnetic waves are radiated whenever charges accelerate as for example for the electrón.Then, this electromagnetic radiation (photons) produces a decrease in the mass of the electron which is given by the formula of the Variant Mass for an Accelerated Charged Particle which was demonstrated by me at this research.Therefore, an additional objective of this article is to demonstrate by theory, calculations and results the discovered formula which describe exactly the variant mass of an accelerated charged particle.This charged particle emits electromagnetic radiation which is called the Maxwell Radiation.Also, the article analyzes and establishes about the effects of the variant mass on the particle.In addition, the formula is tested with the electromagnetic radiation emitted for an electron when leaves from the atom.Finally, it is obtained the formula for the power energy emitted for an Accelerated Charged Particle.
Introduction The propagation of light in periodically ordered photonic crystals bears a strong analogy to the wave propagation of conduction electrons in atomic crystals. The development of Bloch modes and dispersion are determined by the interference of waves that are diffracted by lattice planes [19, 52]. The periodicity commensurate with the wavelength (a ≈ λ/2) gives rise to Bragg diffraction that is associated with frequency windows for which waves are forbidden to propagate in a particular direction. Such stop gaps have long been known to arise for electromagnetic waves, notably for X-rays in atomic crystals [214]. At optical frequencies, the stop gaps that occur in one-dimensional periodic structures, known as Bragg stacks, are widely used in optical laboratories as broadband highly reflecting dielectric mirrors [556]. The distinguishing feature of three-dimensional (3D) photonic crystals is that a common stop gap can be achieved for all directions and for all polarizations simultaneously: the widely pursued 3D photonic band gap . Historically a 3D band gap has never been considered for the propagation of X-rays in periodic media, since a gap requires a high refractive index contrast of order unity, whereas the refractive index varies by less then 10 −4 in the X-ray range. At frequencies inside the 3D photonic band gap, the density of optical states (DOS) completely vanishes. As the density of states can also be interpreted as the density of vacuum fluctuations [334], a 3D band gap thus serves as an effective shield to these fluctuations. The total absence of optical modes in a photonic band gap has implications beyond classical optics that break the analogy between the behavior of light in photonic crystals and the behavior of electrons in atomic crystals. 3D photonic band gap crystals play an important role in cavity quantum electrodynamics (cQED) [64, 549], where they offer at least five prospects for new physics. Firstly, probably the most eagerly pursued phenomenon is the complete inhibition of spontaneous emission: an excited quantum emitter – such as an atom, molecule, or quantum dot – embedded in a crystal with its transition frequency tuned to within the 3D band gap remains forever excited since it cannot decay to the ground state by emitting a photon.
Abstract The new wave mechanics has been eminently successful in correlating and accounting for the large amount of experimental data on the periodic properties of the atom. The applications of the new theory to aperiodic phenomena, though not nearly so numerous, have been attended with no less success; indeed, it is in these experiments on free electrons, in which diffraction patterns similar to those produced by beams of X-rays and light are obtained, that the wave nature of electrons is so clearly and objectively demonstrated. Such diffraction effects have been obtained by a number of investigators by scattering beams of homogeneous electrons in crystals, thin films and by a ruled grating. Similar effects are obtained when electrons are scattered by complex molecules, owing to the symmetrically situated nuclei in the molecular structure, and when α-particles are scattered by helium owing to interference between the waves of the scattered incident particles and recoiling helium nuclei.
Experiment has shown that scattered x-rays contain both a coherent and an incoherent portion. Classical electron theory provides a formula for scattering closely similar to that based on wave mechanics, but includes both coherent and incoherent components only if the atom consists of discrete electrons. From a comparison of the classical and wave-mechanics theories of scattering it is concluded that the most accurate classical analog of Schr\"odinger's $\ensuremath{\psi}{\ensuremath{\psi}}^{*}$ is the probability of occurrence of discrete electrons, and that a particular electron is associated with each particular function ${\ensuremath{\psi}}_{n}{{\ensuremath{\psi}}_{n}}^{*}$.
Studies of the scattering of light on systems of identical atoms under conditions of their quantum degeneracy have been reviewed. The formation of a periodic spatial structure caused by the interference of material waves is responsible for coherent resonance scattering similar to Bragg diffraction on regular spatial inhomogeneities. The interference of macroscopic material waves that is observed in experiments with a Bose–Einstein condensate forms a dielectric medium in the region of optical transparency of the sample that has the properties of a photonic crystal. Common characteristics and differences between the scattering of light on atomic systems under quantum degeneracy conditions and scattering on one-dimensional atomic lattices where the positions of atoms are described by classical statistics have been discussed.