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European Journal of Physics

Electron scattering from a shielded solenoid

Francisco Vera, Ivan A. Schmidt

Published Jul 1, 1991• 0 citations
Publisher

Abstract

The authors consider electron scattering from an infinitely long solenoid of arbitrarily small radius (Aharonov-Bohm scattering), but in which the solenoid is shielded from the beam of a thin absorbing plate. This physical configuration could be accessible to experimental measurement. The analysis is done using a generalization of the Glauber eikonal version of the optical model, for cases in which there is a vector potential present.

DOI
10.1088/0143-0807/12/4/004

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The authors consider electron scattering from an infinitely long solenoid of arbitrarily small radius (Aharonov-Bohm scattering), but in which the solenoid is shielded from the beam of a thin absorbing plate. This physical configuration could be accessible to experimental measurement. The analysis is done using a generalization of the Glauber eikonal version of the optical model, for cases in which there is a vector potential present.
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 quantum-mechanical problems of electron scattering by an infinitely thin solenoid and by a half of an infinitely thin solenoid are examined from the viewpoint of constructing a self-adjoint Hamiltonian. It is demonstrated that in both problems there exist unique self-adjoint operators with a ``non-singular'' domain, that, due to physical reasons, are identified with the corresponding Hamiltonians. In the case of quantized values of magnetic flow along the solenoid, the electron does not experience any scattering by the string. It is shown that the scattering amplitude and wave function of an electron in the problem of scattering by an infinitely long solenoid of radius a in the limit a->0 turn into the corresponding expressions for the problem of an infinitely thin solenoid. In particular, at a quantized value of magnetic flow along the solenoid, scattering disappears at a->0.
The non-stationary Aharonov-Bohm effect (scattering of electron in the field of a narrow solenoid with alternating current) is considered. Using the eikonal approximation, the wave function of electron, the differential and total scattering cross sections are found. Unlike the case of direct current, the total cross section in the case of alternating current turns out to be finite. An oscillating asymmetry in the differential scattering cross section is discovered. The possibility of experimental observation of the effect is discussed.