Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

大阪教育大学紀要. III, 自然科学

Diffraction Scattering of Elementary Particles

Moriyasu Murai, Yujiro Kakudo, Moriyasu Murai, ユウジロウ カクド

Published Jan 1, 1970• 0 citations
OpenAlex

Abstract

The amplitude for diffraction scattering due to an absorbing corpuscle is calculated by using Kirchhoff's formula in optics and the spherical wave expansion. The relationship between the amplitude obtained by us and the usual one used in the general theory of scattering is investigated.

Related papers

Stochastic Model of Microparticle Scattering on a Crystal

Mikhail Batanov-Gaukhman

In this paper, based on the analysis of the formula (2.2) for calculating the elastic scattering diagrams of microparticles on a multilayer crystal surface, derived by the author in the article [3], it is shown that the stochastic approach to solving the problem of scattering of elementary particles on crystals can serve as an alternative to the Louis de Broglie hypothesis about the wave properties of material particles. The results of calculations by formula (2.2), presented in this pa-per, are in good agreement with the experimentally obtained electron diffraction patterns and X-ray diffraction patterns and the Davisson-Germer experiments.

arXiv:2110.00372•Sep 25, 2021•0 citations

Application of the generalized scattering amplitude in quantum potential scatterings

R. T. Ling

The concept of a generalized scattering amplitude is introduced and applied to quantum potential scatterings. After an outgoing spherical wave is factored out from a wave function, the remaining wave envelope is defined as the generalized scattering amplitude. The transformed Schr\"odinger equation, in terms of the generalized scattering amplitude, can be solved numerically by using a finite-difference method over the entire scattering domain. Example problems of scatterings by a spherical potential well and the (${\mathit{e}}^{\mathrm{\ensuremath{-}}}$,H) static field interaction potential are solved to validate the theoretical formulation and numerical method. The far-field solutions for the ordinary scattering amplitude and differential cross section agree very well with those obtained from the partial-wave analysis. The radial profiles of the generalized scattering amplitude and particle density function over the entire scattering region are also presented, and their properties are discussed. These results demonstrate that the method can be used to yield a complete and accurate solution to scattering problems involving arbitrary interaction potentials.

Physical Review A•Jul 1, 1994•4 citations

Fresnel diffraction is a basic quantum mechanical effect

Mohammad Taghi Tavassoly

Using the Fresnel–Kirchhoff integral, we express the state of the light that diffracts from an aperture to a point, by superposition of two or more waves. The amplitudes of the waves are determined by the distances of the point from the ray optics borders of the emerging beams. The interference approach to the Fresnel diffraction leads to a universal formulation of the normalized intensity distribution on the diffraction pattern that determines the state of the incident light, the parameters of the aperture, and its distance from the observation plane, uniquely. In the photon approach, according to the uncertainty principle, confining the position of a photon to an aperture changes the probable propagation direction of the photon in an interval that leads to the diffraction of the photon or light. Thus, the normalized intensity distribution on the diffraction pattern is the probability distribution of a photon. To this probability distribution, a probability amplitude distribution is associated that diffracts similar to a wave in Fresnel diffraction. Applying the introduced approach to the study of the diffraction, from different simple apertures and phase steps, we deduce general behaviors of the Fresnel diffraction and show it is involved in all aspects of light phenomena.

Journal of the Optical Society of America B•May 14, 2021•8 citations

Elastic Scattering Theory

Ana Marı́a Cetto, Luis de la Peña

Chapter 18 is entirely devoted to the quantum theory of scattering, which is normally covered in more detail in a course on quantum field theory. We introduce the main concepts, including scattering amplitude, differential and total cross sections, and form factors, and derive the main formulas for elastic scattering, in a nonrelativistic framework; this allows us to appreciate how the information obtained from scattering experiments is used to explore the intricacies of quantum particles that are otherwise inaccessible. The Born approximation is studied and applied to scattering by a periodic potential, a weak potential, and Rutherford scattering. The partial wave expansion is derived and applied to obtain the optical theorem. The chapter concludes with a complementary section on resonant scattering.

Cambridge University Press eBooks•Dec 18, 2025•0 citations

UNIFORM SEMICLASSICAL APPROXIMATION FOR ABSORPTIVE SCATTERING SYSTEMS

Mahir Saleh Hussein, Mauricio Porto Pato

The uniform semiclassical approximation of the elastic scattering amplitude is generalized to absorptive systems. An integral equation is derived which connects the absorption-modified amplitude to the absorption-free one. Division of the amplitude into diffractive and refractive components is then made possible. Relevance of our formalism to the algebraic approach to scattering theory is pointed out.

Modern Physics Letters A•Apr 1, 1988•1 citation

Quantum theory of neutron double-slit diffraction

Xiao-Jing Liu, Baijun Zhang, Haibo Li +5 more

By solving Schrdinger equation exactly, we obtain the neutron wave function in the slit. With the Kirchhoff’s law, we obtain the neutron diffraction function. Finally, we obtain the mathematical relation between the relative diffraction intensity of neutron double-slit diffraction and the diffraction position. The calculation result is in accordance with the experimental data.

Acta Physica Sinica•Jan 1, 2010•0 citations
In this paper, based on the analysis of the formula (2.2) for calculating the elastic scattering diagrams of microparticles on a multilayer crystal surface, derived by the author in the article [3], it is shown that the stochastic approach to solving the problem of scattering of elementary particles on crystals can serve as an alternative to the Louis de Broglie hypothesis about the wave properties of material particles. The results of calculations by formula (2.2), presented in this pa-per, are in good agreement with the experimentally obtained electron diffraction patterns and X-ray diffraction patterns and the Davisson-Germer experiments.
The concept of a generalized scattering amplitude is introduced and applied to quantum potential scatterings. After an outgoing spherical wave is factored out from a wave function, the remaining wave envelope is defined as the generalized scattering amplitude. The transformed Schr\"odinger equation, in terms of the generalized scattering amplitude, can be solved numerically by using a finite-difference method over the entire scattering domain. Example problems of scatterings by a spherical potential well and the (${\mathit{e}}^{\mathrm{\ensuremath{-}}}$,H) static field interaction potential are solved to validate the theoretical formulation and numerical method. The far-field solutions for the ordinary scattering amplitude and differential cross section agree very well with those obtained from the partial-wave analysis. The radial profiles of the generalized scattering amplitude and particle density function over the entire scattering region are also presented, and their properties are discussed. These results demonstrate that the method can be used to yield a complete and accurate solution to scattering problems involving arbitrary interaction potentials.
Using the Fresnel–Kirchhoff integral, we express the state of the light that diffracts from an aperture to a point, by superposition of two or more waves. The amplitudes of the waves are determined by the distances of the point from the ray optics borders of the emerging beams. The interference approach to the Fresnel diffraction leads to a universal formulation of the normalized intensity distribution on the diffraction pattern that determines the state of the incident light, the parameters of the aperture, and its distance from the observation plane, uniquely. In the photon approach, according to the uncertainty principle, confining the position of a photon to an aperture changes the probable propagation direction of the photon in an interval that leads to the diffraction of the photon or light. Thus, the normalized intensity distribution on the diffraction pattern is the probability distribution of a photon. To this probability distribution, a probability amplitude distribution is associated that diffracts similar to a wave in Fresnel diffraction. Applying the introduced approach to the study of the diffraction, from different simple apertures and phase steps, we deduce general behaviors of the Fresnel diffraction and show it is involved in all aspects of light phenomena.
Chapter 18 is entirely devoted to the quantum theory of scattering, which is normally covered in more detail in a course on quantum field theory. We introduce the main concepts, including scattering amplitude, differential and total cross sections, and form factors, and derive the main formulas for elastic scattering, in a nonrelativistic framework; this allows us to appreciate how the information obtained from scattering experiments is used to explore the intricacies of quantum particles that are otherwise inaccessible. The Born approximation is studied and applied to scattering by a periodic potential, a weak potential, and Rutherford scattering. The partial wave expansion is derived and applied to obtain the optical theorem. The chapter concludes with a complementary section on resonant scattering.