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

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Comments on the Born approximation in Aharonov-Bohm Scattering

Bengt Nagel

Published Dec 15, 1985• 18 citations
Publisher

Abstract

The cylindrically symmetric partial-wave amplitude for scattering of an electron on an impenetrable infinite solenoid of finite radius is studied for small magnetic-flux values and an electron wavelength much larger than the solenoid radius. The results of a recent study for the Born series expression of this amplitude is discussed.
DOI
10.1103/physrevd.32.3328

Related papers

Aharonov-Bohm effect as a scattering event

Yakir Aharonov, C. K. Au, E. C. Lerner +1 more

The Aharonov-Bohm effect is reconsidered as a scattering event of an electron by a magnetic field confined in an infinite solenoid of finite radius both in the situation where the solenoid is penetrable as well as impenetrable. We next discuss the validity of the Born approximation for the partial-wave scattering amplitudes and explain why for the cylindrically symmetric $(m=0)$ partial wave the first Born approximation fails in the long-wavelength limit or as the radius of the solenoid shrinks to zero.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•May 15, 1984•58 citations

On the application of the Born approximation to the Aharonov-Bohm and related problems

R A Brown

The exact solution to the problem of scattering of electrons by a solenoid of infinite length is studied in two limiting cases; firstly, when the radius r 0 to 0 with the enclosed flux phi held constant, and secondly, when phi to 0 with r 0 held constant. Previously reported discrepancies between the Born approximation and the Aharonov-Bohm solution of this problem are reconciled and conditions for the validity of each of these two approximations are established. The relevance of the results to a related scattering problem involving crystal dislocations is briefly discussed and in this case the Born approximation is shown to be valid over almost all the Fermi surface.

Journal of Physics A Mathematical and General•Sep 11, 1985•16 citations

Modified solenoid scattering for the Aharonov-Bohm effect

R A Brown

A method of partial-wave analysis is used to extend the treatment of Aharonov and Bohm (1959) for the scattering from an unscreened solenoid of infinitesimal radius to include screening and non-zero radius. The method yields a scattering amplitude which bears a formal resemblance to that appropriate to modified Coulomb scattering. The scattering amplitude and the momentum transfer cross section retain a dependence on the enclosed flux as the screening barrier becomes infinite, resulting in a component of force, periodic in the enclosed flux, being exerted on the barrier. The resulting implications concerning the locality of electromagnetic interactions are discussed. The force is shown to persist when the conditions of strict impenetrability are relaxed and the possibility of directly observing this quantum force is examined.

Journal of Physics A Mathematical and General•Aug 1, 1987•4 citations

Aharonov-Bohm scattering by a thin impenetrable solenoid

E. Corinaldesi, F. Rafeli

Aharonov and Bohm constructed a wave function describing scattering of electrons by an impenetrable solenoid, from which they derived a cross section of the form dσ/dϑ = g (ϑ)sin2(πα), where ϑ is the scattering angle and α is a coupling constant. A simplified version of their work is presented, together with an attempt to obtain by Born approximation the approximate expression dσ/dϑ ? g (ϑ) π2α2 small α. It is explained why such an attempt is unsuccessful.

American Journal of Physics•Nov 1, 1978•43 citations

Helicity and the Aharonov-Bohm effect

Francisco Vera, Ivan A. Schmidt

Conservation of helicity is applied to the scattering of relativistic electrons by an infinitely long solenoid of arbitrarily small radius (Aharonov-Bohm scattering). It is also shown that the Born approximation, which fails when applied to Aharonov-Bohm scattering in the Schr\"odinger equation formalism, gives correct results in the case of the Dirac equation.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Nov 15, 1990•26 citations

Scattering of a charged particle from a hard cylindrical solenoid: Aharonov-Bohm Effect

Oktay Yilmaz

The scattering amplitude of a charged particle from a long hard cylinderical solenoid is derived by solving the time independent Schrödinger equation on a double connected plane. It is a summation over the angular momentum quantum number (partial wave summation). It is shown that only negative mechanical angular momenta contribute to the amplitude when the radius of the solenoid goes to zero limit without varying the magnetic induction flux (Flux line). Original Aharonov-Bohm result is obtained with this limit.

arXiv:1311.6924•Chinese Journal of Physics•Nov 27, 2013•2 citations
The Aharonov-Bohm effect is reconsidered as a scattering event of an electron by a magnetic field confined in an infinite solenoid of finite radius both in the situation where the solenoid is penetrable as well as impenetrable. We next discuss the validity of the Born approximation for the partial-wave scattering amplitudes and explain why for the cylindrically symmetric (m=0)(m=0)(m=0) partial wave the first Born approximation fails in the long-wavelength limit or as the radius of the solenoid shrinks to zero.
The exact solution to the problem of scattering of electrons by a solenoid of infinite length is studied in two limiting cases; firstly, when the radius r 0 to 0 with the enclosed flux phi held constant, and secondly, when phi to 0 with r 0 held constant. Previously reported discrepancies between the Born approximation and the Aharonov-Bohm solution of this problem are reconciled and conditions for the validity of each of these two approximations are established. The relevance of the results to a related scattering problem involving crystal dislocations is briefly discussed and in this case the Born approximation is shown to be valid over almost all the Fermi surface.
A method of partial-wave analysis is used to extend the treatment of Aharonov and Bohm (1959) for the scattering from an unscreened solenoid of infinitesimal radius to include screening and non-zero radius. The method yields a scattering amplitude which bears a formal resemblance to that appropriate to modified Coulomb scattering. The scattering amplitude and the momentum transfer cross section retain a dependence on the enclosed flux as the screening barrier becomes infinite, resulting in a component of force, periodic in the enclosed flux, being exerted on the barrier. The resulting implications concerning the locality of electromagnetic interactions are discussed. The force is shown to persist when the conditions of strict impenetrability are relaxed and the possibility of directly observing this quantum force is examined.
The scattering amplitude of a charged particle from a long hard cylinderical solenoid is derived by solving the time independent Schrödinger equation on a double connected plane. It is a summation over the angular momentum quantum number (partial wave summation). It is shown that only negative mechanical angular momenta contribute to the amplitude when the radius of the solenoid goes to zero limit without varying the magnetic induction flux (Flux line). Original Aharonov-Bohm result is obtained with this limit.