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 A

Neutron scattering in the magnetic field of a linear current: Exact S matrix and cross section

Vladimir I. Osherov, V. G. Ushakov

Published May 14, 2004• 1 citation
Publisher

Abstract

The problem of the neutron scattering in the magnetic field of a linear current has been formulated and solved quantum mechanically exactly. The $S$ matrix has been derived in the adiabatic representation and the closed analytical expression for the differential cross section has been obtained. The results reveal the topological phase part at the nonadiabatic collisions.

DOI
10.1103/physreva.69.052710

Related papers

Neutron in the magnetic field of a linear conductor with current as an example of the two-dimensional supersymmetric problem

A. I. Voronin

The exact solution is presented for the quantum-mechanical problem of a neutron interacting with the magnetic field of a linear conductor with current. It is shown that this problem has a supersymmetry. The energy spectrum and eigenfunctions are derived in a closed form using this supersymmetry.

Physical Review A•Jan 1, 1991•35 citations

Classical limit for the scattering of Dirac particles in a magnetic field

G Murgu a, M Moreno

We present a relativistic quantum calculation at first order in perturbation theory of the differential cross section for a Dirac particle scattered by a solenoidal magnetic field. The resulting cross section is symmetric in the scattering angle as those obtained by Aharonov and Bohm (AB) in the string limit and by Landau and Lifshitz (LL) for the non-relativistic case. We show that taking pr 0 |sin (θ/2)|/ ≪ 1 in our expression of the differential cross section it reduces to the one reported by AB, and if additionally we assume θ ≪ 1 our result becomes the one obtained by LL. However, these limits are explicitly singular in as opposed to our initial result. We analyse the singular behaviour in and show that the perturbative Planck limit ( → 0) is consistent, in contrast to those of the AB and LL expressions. We also discuss the scattering in a uniform and constant magnetic field, which resembles some features of QCD.

arXiv:quant-ph/0211195•Journal of Physics A Mathematical and General•Feb 26, 2003•1 citation

Quantum states of neutrons bound in the magnetic field of a rectilinear current

R. Blümel, Klaus Dietrich

The spectrum and the wave functions of neutrons bound in the magnetic field of a thin rectilinear current filament are calculated analytically by solving a fourth-order Hamburger equation. Finite current cross sections are treated numerically: the bound states persist---a necessary prerequisite in view of possible experimental verifications of the theory. Two setups [(i) a superconducting wire and (ii) a Church trap] are proposed for obtaining these states experimentally. Some results on spin-1 magnetic surface states are presented.

Physical Review A•Jan 1, 1991•98 citations

Quantum effects in the scattering by the magnetic field of a solenoid

Gabriela Murguía, Moreno, Matias

We present a relativistic quantum calculation at first order in perturbation theory of the differential cross section for a Dirac particle scattered by the magnetic field of a solenoid. The resulting cross section is symmetric in the scattering angle as those obtained by Aharonov and Bohm (AB) in the string limit and by Landau and Lifshitz (LL) for the non relativistic case. We show that taking pr_0 sin(theta/2) << 1 in our expression of the differential cross section it reduces to that one reported by AB, and if additionally we assume theta << 1 our result becomes the one obtained by LL. However, these limits are explicitly singular in hbar as opposed to our initial result. We analyse the singular behavior in hbar and show that the perturbative Planck limit (hbar -> 0) is consistent, contrarily to those of the AB and LL expressions.

arXiv:physics/0202020•Feb 7, 2002•0 citations

Aharonov-Bohm scattering on two parallel flux tubes of the same magnetic flux

Zhi-Yu Cu, Qian Shang-Wu

The problem of Aharonov-Bohm scattering on two parallel flux tubes of the same magnetic flux is solved exactly and the differential cross section is calculated.

Journal of Physics A Mathematical and General•Sep 21, 1990•2 citations

The neutron Berry phase

V. K. Ignatovich

The neutron Berry phase is found from an exact analytic solution of the Schrödinger equation in a constant magnetic field and a perpendicular radiofrequency field rotating with an angular frequency . The solution is found for arbitrary values of , , and . The Berry phase is shown to be a linear approximation of the exact value in the parameter when this parameter is small.

Physics-Uspekhi•Jun 8, 2013•4 citations
The problem of the neutron scattering in the magnetic field of a linear current has been formulated and solved quantum mechanically exactly. The SSS matrix has been derived in the adiabatic representation and the closed analytical expression for the differential cross section has been obtained. The results reveal the topological phase part at the nonadiabatic collisions.
We present a relativistic quantum calculation at first order in perturbation theory of the differential cross section for a Dirac particle scattered by a solenoidal magnetic field. The resulting cross section is symmetric in the scattering angle as those obtained by Aharonov and Bohm (AB) in the string limit and by Landau and Lifshitz (LL) for the non-relativistic case. We show that taking pr 0 |sin (θ/2)|/ ≪ 1 in our expression of the differential cross section it reduces to the one reported by AB, and if additionally we assume θ ≪ 1 our result becomes the one obtained by LL. However, these limits are explicitly singular in as opposed to our initial result. We analyse the singular behaviour in and show that the perturbative Planck limit ( → 0) is consistent, in contrast to those of the AB and LL expressions. We also discuss the scattering in a uniform and constant magnetic field, which resembles some features of QCD.
The spectrum and the wave functions of neutrons bound in the magnetic field of a thin rectilinear current filament are calculated analytically by solving a fourth-order Hamburger equation. Finite current cross sections are treated numerically: the bound states persist---a necessary prerequisite in view of possible experimental verifications of the theory. Two setups [(i) a superconducting wire and (ii) a Church trap] are proposed for obtaining these states experimentally. Some results on spin-1 magnetic surface states are presented.
We present a relativistic quantum calculation at first order in perturbation theory of the differential cross section for a Dirac particle scattered by the magnetic field of a solenoid. The resulting cross section is symmetric in the scattering angle as those obtained by Aharonov and Bohm (AB) in the string limit and by Landau and Lifshitz (LL) for the non relativistic case. We show that taking pr_0 sin(theta/2) << 1 in our expression of the differential cross section it reduces to that one reported by AB, and if additionally we assume theta << 1 our result becomes the one obtained by LL. However, these limits are explicitly singular in hbar as opposed to our initial result. We analyse the singular behavior in hbar and show that the perturbative Planck limit (hbar -> 0) is consistent, contrarily to those of the AB and LL expressions.