A scattering model describing the interaction between charged particles and a set of rigid neutral atoms was developed to demonstrate that particle theory could predict charged particles diffraction in materials composed of neutral atoms. A ring of gold atoms with a planar distribution of atomic electrons was used as the target. Electrons, positrons, neutrons, anti-neutrons and photons showed theoretical evidence of diffraction. The results of the calculations show signs of Poisson-Arago spot formation with spot not only behind the ring but also in front of it and these spots appeared independently of the projectile charge. This finding agrees with wave and quantum mechanics theory but the fact that a deflection at the edge of a ring of atoms is obtained using classical electrostatics and a quasi-quantum mechanical model for the atomic electrons, indicates that the wave (quantum) theory is not necessary to explain diffraction and if we take into account that the wave theory cannot explain the black body radiation, neither the photoelectric effect and nor the Compton effect, then the particle theory of diffraction is put in a strong solid grounds. Due to the importance of this matter in theoretical physic and gravitation, it is worthy to implement simulating conditions (using full size modeling) to compare the results with experimental data.
A scattering model describing the interaction between charged particles and a set of rigid neutral atoms was developed to demonstrate that particle theory could predict charged particles diffraction in materials composed of neutral atoms. A ring of gold atoms with a planar distribution of atomic electrons was used as the target. Electrons, positrons, neutrons, anti-neutrons and photons showed theoretical evidence of diffraction. The results of the calculations show signs of Poisson-Arago spot formation with spot not only behind the ring but also in front of it and these spots appeared independently of the projectile charge. This finding agrees with wave and quantum mechanics theory but the fact that a deflection at the edge of a ring of atoms is obtained using classical electrostatics and a quasi-quantum mechanical model for the atomic electrons, indicates that the wave (quantum) theory is not necessary to explain diffraction and if we take into account that the wave theory cannot explain the black body radiation, neither the photoelectric effect and nor the Compton effect, then the particle theory of diffraction is put in a strong solid grounds. Due to the importance of this matter in theoretical physic and gravitation, it is worthy to implement simulating conditions (using full size modeling) to compare the results with experimental data.
In an analysis of experiments famous for particle models of light and charge, a non-classical wave model is developed to explain these particle-like properties in terms of waves. The experiments and issues examined include: charge diffraction, charge quantization, photoelectric effect, Compton effect, black body radiation, spin, and antimatter. The model has three postulates: (a) a threshold concept whereby charge, mass, and action are maximums at e, m e , and h respectively, (b) a ratio concept whereby free space measures of e, m e , and h will always reveal themselves in ratios e/m, e/h, or h/m, allowing components of these ratios to individually diminish as the wave spreads while the ratio value remains intact, and (c) an envelope property of the Ψ wave (Schrodinger’s amplitude) whereby the envelope is full and stable with a graphic area of h. The envelope concept is developed by replacing the phase wavelength in de Broglie’s equation with the group length. Some conclusions: Our constants h, e, and m e , can only be independently measured in atoms or collisions where the envelopes are full, but not in free-space diffraction, or in deflection experiments. The particle-like properties of charge are explained with envelopes displacing each other in space as they reach threshold h. Particles of light then become an illusion of these threshold and ratio properties of the charge-wave.
Since de Broglie’s famous postulation of the wave-nature of material particles and its subsequent experimental verification, it is known that atoms and molecules behave like waves on a small scale. The investigation of matter waves is a fundamental topic in quantum mechanics. Furthermore, matter waves have many applications in a number of scientific fields. For example they are used to investigate materials by studying the diffraction of atoms (Helium Atom Scattering) or electrons (Low-energy electron-diffraction) from the material’s surface. The topic of this thesis has been to make nano-structured optical elements for matter-waves and use them in a number of experiments. A major result of this thesis is the performance of the classical Poisson-spot experiment with neutral matter-waves. The Poisson-spot refers to the bright interference spot observed in the shadow of a circular obstacle. The experiment gave convincing evidence of the wave nature of light at the beginning of the 19th century. The first two articles (A&B) in this thesis are concerned with the Poisson-spot experiment for matter waves and its applications. The experiment was performed using low-energy deuterium molecules (normal D2, 23.5 meV), which is described in the first article. In the second article the feasibility of using the Poisson-spot experiment to demonstrate the wave-nature of large molecules is studied. The wave properties of large molecules are an important topic in current research. The remaining three articles are concerned with Fresnel zone-plates. Fresnel zoneplates are axially symmetric diffraction gratings that can be used to focus waves. Loosely formulated the relationship between Fresnel zone-plates and the circular object in the Poissonspot experiment is the same as the relationship between multiple-slit gratings and a single straight edge. Paper C studies the application of microscopy with neutral atoms and molecules and the limitations of focusing matter waves with zone plates. The fabrication of the nanostructured free-standing zone-plates using electron-beam lithography is the topic of paper D. A second, new application of Fresnel zone-plates is introduced in paper E: There a zone plate is used for a direct size measurement of the so-called virtual source in a supersonic expansion. The main-result from the Poisson-spot experiment was the observation of the Poisson spot with a molecular-deuterium beam and the successful comparison of the collected experimental data with Fresnel-diffraction theory. The wave-length independence of the on-axis interferencecondition in the Poisson-spot experiment and the weak constraints on angular alignment and position of the circular object led us to conclude that the Poisson spot is a good candidate for demonstrating the wave nature of larger molecules. This idea is studied further in paper B, where among other things the feasibility of a Poissonspot experiment with the fullerene molecule C70 is examined. The main conclusion from this article was that the wave-nature of a molecular-beam can be demonstrated in diffraction experiments with circular discs that have varying amount of intended edge-corrugation. This is because the dependence of the bright spot on the edge-corrugation in the particle-model is different than in the wave-model. The result for the C70 Poisson-spot was that the experiment would be very challenging with count rates as low as 10−4 s−1. However, one possibility would be, due to the simplicity of the setup, to parallelize the experiment and measure the diffraction pattern behind many circular discs at once. This could be realized using the fabrication techniques discussed in chapter 4. Other applications of the Poisson spot could include the study of the Casmir-Polder potential, molecule-lithography and diffraction experiments with atom-lasers from Bose-Einstein condensates. While Fresnel zone-plates can be used to focus any type of wave they suffer from strong chromatic aberration since their focal length is inversely proportional to wavelength. In the case of neutral atom and molecule focusing this is what limits resolution. Paper C presents the highest resolution helium transmission-images hitherto and results from the first focusing of molecular deuterium with a zone plate. In addition the paper discusses the resolution-limit and finds that with presently available techniques a minimal spot size of 300 nm full-width-athalf- maximum is feasible using a zone plate of 200 μm diameter and a beam with speed ratio of about 500. The Fresnel zone-plates used to focus the supersonic-expansion beams need to be freestanding, since the low-energy atoms and molecules do not penetrate any material. In paper D an electron-beam lithography fabrication-process for free-standing zone-plates is presented. The process uses a 200-nm-thin layer of low-stress silicon-nitride for the material of the zone plates. The fabricated zone plates were tested in the supersonic-expansion beam apparatus. The transmission and first-order diffraction-efficiency are close to the theoretical prediction for the smaller 190 μm-diameter zone plates patterned with a single electron-beam write-field. A reduction to 70 % for the 388-μm-diameter zone-plate was observed which was attributed to stitching errors since it was stitched together from four write-fields. In chapter 4 additional unpublished results are presented on spatial-phase-locked electron-beam lithography, which aims at the reduction of stitching errors and other pattern-placement errors in electron-beam lithography. Finally in paper E one of the fabricated zone plates in addition to a previously existing one is used to measure the virtual source-width of a molecular deuterium supersonic-expansion beam. The virtual source-width is a measure of the beam’s temperature perpendicular to the beam axis. The beam’s energy distribution along the beam axis is measured using the timeof- flight method. Data sets for source temperatures T0=310 K and T0=106 K were collected in the stagnation pressure ranges p0=3-171 bar and p0=3-131 bar, respectively. The measured parameters were compared to a simple model of the expansion which explicitly includes the coupling between translational and rotational degrees of freedom. The data generally corresponded very well to the model, except for the virtual source size which was systematically about 2/3 of the model’s prediction. For the cold source-conditions the beam is increasingly heated due to condensation effects at increasing pressures, which results in a clear deviation from the model. This could be used to estimate the fraction of condensed molecules in the beam.
Diffraction of matter waves is an important demonstration of the fact that objects in nature possess a mixture of particlelike and wavelike properties. Unlike in the case of light diffraction, matter waves are subject to a vacuum-mediated interaction with diffraction obstacles. Here we present a detailed account of this effect through the calculation of the attractive Casimir-Polder potential between a dielectric sphere and an atomic beam. Furthermore, we use our calculated potential to make predictions about the diffraction patterns to be observed in an ongoing experiment where a beam of indium atoms is diffracted around a silicon-dioxide sphere. The result is an amplification of the on-axis bright feature, which is the matter-wave analog of the well-known ``Poisson spot'' from optics. Our treatment confirms that the diffraction patterns resulting from our complete account of the sphere Casimir-Polder potential are indistinguishable from those found via a large-sphere nonretarded approximation in the discussed experiments, establishing the latter as an adequate model.
Arguments about particles or waves gave way to a recognized need for both particles and waves in the description of radiation. The confusion over particle versus wave properties was resolved by Louis de Broglie. He postulated that since light has a dual wave–particle nature, matter also has this nature. The idea was to perform a diffraction experiment with electrons. An interference pattern was demonstrated not only with electrons, but also with many kinds of material particles like protons and neutrons. However, any attempt to observe an interference pattern with neutral atoms was found difficult by the fact that atoms carried no charge as electrons do and could not penetrate through condensate matter like neutrons. The de Broglie wavelength of an electron in the smallest orbit turns out to be exactly equal to the circumference of the orbit predicted by Bohr. The interpretation of the interference phenomenon becomes more subtle when the light beams are replaced by individual photons or particles.
A mathematical model (the Schrodinger Equation) and a physical model (Spinning Charged Ring Model) of the electron are compared for their ability to predict waves emitted by electrons. Although it is a fundamental postulate of Quantum Mechanics, the Schrodinger Equation does not allow for an interpretation of wave-functions as physical waves, cannot be a com- plete theoretical description of a micro physical system, neglects intrinsic characteristics of particle motion, and fails in several other ways to correspond to physical reality. The Ring Model of Electrons makes accurate and complete predictions of fields and waves by using the locations and internal motions of charge elements that make up the electron in order to determine the external fields of the electron. The physical Ring Model, compli- ant with the law of cause and effect, explains the meaning of Planck's Constant and accu- rately predicts the Photoelectric Effect, wavelengths of hydrogen line spectra, blackbody radiation, and the Compton Wavelength. An unbiased assessment of these facts implies that electrons are small physical particles that closely resemble the Spinning Charged Ring Model, and these electrons are a source of electromagnetic waves.
The mainstream quantum mechanics uses “probability wave superposition and single-electron self-interference” to explain electron single-slit and double-slit diffraction. This theory deviates from the essential nature of real particle interactions and has fundamental logical flaws. The electron is a negatively charged real particle with a definite physical size and high-frequency transverse oscillation; a single real particle has no physical basis for self-interference. Abandoning the abstract probability wave hypothesis, this paper establishes a complete real-interaction model including electrostatic repulsion deflection, surface electron exchange, collision scattering, microscopic refraction, and barrier diffraction, based on the three-dimensional random transverse oscillation and charge repulsion of electrons. The model uniformly explains the real formation mechanism of electron single-slit diffraction and double-slit interference fringes. This paper proves that in single-electron sequential emission, each electron passes through only one slit; all bright and dark fringes are the statistical result of multiple microscopic interactions between electrons and slit walls or the central barrier. The disappearance of fringes under observation is caused by external disturbance to the inherent oscillation and wall-interaction equilibrium, not by wave function collapse. This paper further clarifies that whether an electron can pass through a slit is determined by its transverse oscillation amplitude, not by wavelength. Amplitude directly corresponds to slit width and is the core controlling variable of diffraction. Meanwhile, if no slit is placed, electrons flying directly to the screen produce no diffraction or interference fringes, proving that electrons themselves have no self-interference ability. Fringes are generated by slit structures, not by intrinsic wave interference of electrons. This study corrects the century-long misunderstanding of electron diffraction and establishes a new microscopic diffraction mechanism consistent with classical real-particle physics.