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

Journal of Jiangxi University of Science and Technology

The Born Approximation and Eikonal Approximation of the Quantum Scattering

Liao Yubo

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

The theory of scattering is a very important part of the quantum mechanics.The Born approximation and Eikonal approximation of the Scattering cross-section are calculated with the Gauss potential and Lenz-jensen potential under a particular incident energy.The results show that the bigger the Electronic energy is,the smaller the total scattering crossection is and the weaker the electron scattering of potential field is.There is little influence of potential to the energetic particle about the Lenz-jensen potential.And the majority of scattered particles are concentrated on a narrow range.

Related papers

Applications of the eikonal approximation in quantum mechanical scattering

Barry R. Holstein

Scattering is an important component of any quantum mechanics course. However, the scattering amplitude in the case of a general potential is often calculated using the simple Born approximation, which does not embed general properties such as unitarity or analyticity. We show that a relatively simple extension, the eikonal approximation, offers a significant improvement and demonstrate this in the case of the electromagnetic and gravitational interactions.

American Journal of Physics•May 1, 2023•3 citations

Quantum Theory of Scattering

Arjun Sharma

In this chapter we discuss the quantum theory of scattering of incident particles from the target where an incident beam has point particles, scattering is elastic, the scattering potential is time independent, there is no multiple scattering, and the interaction between an incident particle and a scattering center is described by the potential that depends only on relative positions of particles. Scattering cross-section and frame of reference, asymptotic expansion of wave function and formal expression for scattering amplitude, partial wave analysis, integral equation, and the Born approximation are covered in the chapter, in a broader sense. Free particle and asymptotic solutions, scattering amplitude and phase shift, optical theorem, scattering length, phase shift and its interpretation, scattering by a square well potential and by hard sphere potential, and interpretation of the phase shift and its expression are explained with the use of partial wave analysis. Scattering from bare and screened potentials within the Born approximation, validity of the Born approximation, and the transformation from the center of a mass coordinate system to a laboratory coordinate system are written towards the end of the chapter.

CRC Press eBooks•Jun 18, 2021•19 citations

Research on α-particle scattering with quantum mechanics

Lixia Li

The Rutherford formula cannot explain α-particle's small angle scattering question.This paper deals with this problem using the quantum scattering theory-born approximation,takes account of the influence of the shielding effect of the electron and limited quality of the atomic nucleus to scattering cross-section,carries on the revision to the Rutherford scattering formula according to experimental result.

Journal of Science of Teachers' College and University•Jan 1, 2006•0 citations

Quantum and classical effects at scattering of high energy charged particles in thin crystals

N.F. Shul’ga, S.N. Shulga

The present work reviews the results concerning quantum scattering theory of ultrarelativistic electrons in ultrathin crystals and its comparison with analogous classical results. It deals with an intermediate range of thicknesses, large enough for that the particle motion could not be considered as rectilinear but small enough for that the channeling regime of motion was not established. The quantum theory is based both upon the representation of the scattering amplitude as an integral over the surface surrounding the target, and on the so-called operator method of determination of the wave function as a solution of a Schrödinger-like equation. The latter method implies a wide use of the Fourier technique, both in calculation of each next step in the wave packet evolution, and in moving from the spatial coordinates to the angular ones. The authors compare the quantum differential scattering cross-sections with the classical ones in the considered range of crystal thicknesses and show their resemblances, distinctions and the evolution of these distinctions with the change of the particle energy. The simplest variant of quantum scattering theory based upon the eikonal approximation of quantum mechanics is considered. In the paper the quantum differential scattering cross-section was calculated and its affinity with the classical one was demonstrated. In the preparation of these lecture notes the material of the paper [4] was used.

Resource-Efficient Technologies•Jul 23, 2018•0 citations

A Quantum Theory of Scattering by a Fluctuating Potential

Yutaka Inaba

A quantum-mechanical scattering theory is developed for the scattering by a potential of which strength is randomly fluctuating between two values with a switching rate γ/2. Within this model the T matrix averaged over the fluctuation is derived exactly, from which the averaged scattering cross section (ACS) is obtained by using the optical theorem. Explicit calculations of the ACS are carried out for three cases; (i) within the Born approximation, (ii) for a separable potential, (iii) for a short-range potential in a lattice. It is found that the low-energy ACS is enhanced in comparison with the static case for \(E/\hbar{\lesssim}\gamma{\lesssim}\hbar/(2ma^{2})\) because of the large inelastic cross section, where E is the energy of the incident particle with a mass m and a is the range of the potential.

Journal of the Physical Society of Japan•Apr 1, 1982•1 citation

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
The theory of scattering is a very important part of the quantum mechanics.The Born approximation and Eikonal approximation of the Scattering cross-section are calculated with the Gauss potential and Lenz-jensen potential under a particular incident energy.The results show that the bigger the Electronic energy is,the smaller the total scattering crossection is and the weaker the electron scattering of potential field is.There is little influence of potential to the energetic particle about the Lenz-jensen potential.And the majority of scattered particles are concentrated on a narrow range.
In this chapter we discuss the quantum theory of scattering of incident particles from the target where an incident beam has point particles, scattering is elastic, the scattering potential is time independent, there is no multiple scattering, and the interaction between an incident particle and a scattering center is described by the potential that depends only on relative positions of particles. Scattering cross-section and frame of reference, asymptotic expansion of wave function and formal expression for scattering amplitude, partial wave analysis, integral equation, and the Born approximation are covered in the chapter, in a broader sense. Free particle and asymptotic solutions, scattering amplitude and phase shift, optical theorem, scattering length, phase shift and its interpretation, scattering by a square well potential and by hard sphere potential, and interpretation of the phase shift and its expression are explained with the use of partial wave analysis. Scattering from bare and screened potentials within the Born approximation, validity of the Born approximation, and the transformation from the center of a mass coordinate system to a laboratory coordinate system are written towards the end of the chapter.
The present work reviews the results concerning quantum scattering theory of ultrarelativistic electrons in ultrathin crystals and its comparison with analogous classical results. It deals with an intermediate range of thicknesses, large enough for that the particle motion could not be considered as rectilinear but small enough for that the channeling regime of motion was not established. The quantum theory is based both upon the representation of the scattering amplitude as an integral over the surface surrounding the target, and on the so-called operator method of determination of the wave function as a solution of a Schrödinger-like equation. The latter method implies a wide use of the Fourier technique, both in calculation of each next step in the wave packet evolution, and in moving from the spatial coordinates to the angular ones. The authors compare the quantum differential scattering cross-sections with the classical ones in the considered range of crystal thicknesses and show their resemblances, distinctions and the evolution of these distinctions with the change of the particle energy. The simplest variant of quantum scattering theory based upon the eikonal approximation of quantum mechanics is considered. In the paper the quantum differential scattering cross-section was calculated and its affinity with the classical one was demonstrated. In the preparation of these lecture notes the material of the paper [4] was used.
A quantum-mechanical scattering theory is developed for the scattering by a potential of which strength is randomly fluctuating between two values with a switching rate γ/2. Within this model the T matrix averaged over the fluctuation is derived exactly, from which the averaged scattering cross section (ACS) is obtained by using the optical theorem. Explicit calculations of the ACS are carried out for three cases; (i) within the Born approximation, (ii) for a separable potential, (iii) for a short-range potential in a lattice. It is found that the low-energy ACS is enhanced in comparison with the static case for E/ℏ≲γ≲ℏ/(2ma2)E/\hbar{\lesssim}\gamma{\lesssim}\hbar/(2ma^{2})E/ℏ≲γ≲ℏ/(2ma2) because of the large inelastic cross section, where E is the energy of the incident particle with a mass m and a is the range of the potential.
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.