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arXiv:quant-ph/9901066 · Physical Review A

Aharonov-Bohm scattering of charged particles and neutral atoms: The role of absorption

Jürgen Audretsch, Vladimir D. Skarzhinsky

Published Sep 1, 1999• 16 citations
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Abstract

The Aharonov-Bohm (AB) scattering of charged particles by the magnetic field of an infinitely long and infinitely thin solenoid (magnetic string) in an absorbing medium is studied. We discuss the partial-wave approach to this problem and show that the standard partial-wave method can be adjusted to this case. The effect of absorption leads to oscillations of the AB cross section. Based on this we investigate the scattering of neutral atoms with induced electric dipole moments by a charge wire of finite radius, which is placed in a uniform magnetic field. The physical realistic and practically important case that all atoms that collide with the wire are totally absorbed at its surface is studied in detail. The dominating terms of the scattering amplitude are evaluated analytically for different physical constellations. The remaining terms are written in a form suitable for a numerical computation. We show that if the magnetic field is absent, the absorbing charged wire causes oscillations of the cross section. In the presence of the magnetic field the cross section increases and the dominating Aharonov-Bohm peak appears in the forward direction, suppressing the oscillations.

DOI
10.1103/physreva.60.1854

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Europhysics Letters (EPL)•May 20, 1997•33 citations
The Aharonov-Bohm (AB) scattering of charged particles by the magnetic field of an infinitely long and infinitely thin solenoid (magnetic string) in an absorbing medium is studied. We discuss the partial-wave approach to this problem and show that the standard partial-wave method can be adjusted to this case. The effect of absorption leads to oscillations of the AB cross section. Based on this we investigate the scattering of neutral atoms with induced electric dipole moments by a charge wire of finite radius, which is placed in a uniform magnetic field. The physical realistic and practically important case that all atoms that collide with the wire are totally absorbed at its surface is studied in detail. The dominating terms of the scattering amplitude are evaluated analytically for different physical constellations. The remaining terms are written in a form suitable for a numerical computation. We show that if the magnetic field is absent, the absorbing charged wire causes oscillations of the cross section. In the presence of the magnetic field the cross section increases and the dominating Aharonov-Bohm peak appears in the forward direction, suppressing the oscillations.
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 wave functions that describe scattering of a charged particle by a confined magnetic field (Aharonov-Bohm effect) and by a Coulomb field are analyzed. It is well known that the usual procedure of finding asymptotic forms of these functions which admit a separation into a superposition of an incident plane wave and a circular or spherical scattered wave is problematic near the forward direction. It thus appears to be impossible to express the conservation of probability by means of an optical theorem of the usual kind. Both the total cross section and the forward scattering amplitude appear to be infinite. To address these difficulties we find a new representation for the asymptotic form of the Aharonov-Bohm wave function that is valid for all angles. Rather than try to define a cross section at forward angles, however, we work instead with the probability current and find that it is quite well behaved. The same is true for Coulomb scattering. We trace the usual difficulties to a nonuniformity of limits.
The scattering of relativistic spin-1/2 neutral particles with a magnetic dipole moment by a long straight charged line and a magnetic flux line at the same position is studied. The scattering cross sections for unpolarized and polarized particles are obtained by solving the Dirac-Pauli equation. The results are in general the same as those for pure Aharonov-Casher scattering (by the charged line alone) as expected. However, in special cases when the incident energy, the line charge density, and the magnetic flux satisfy some relations, the cross section for polarized particles is dramatically changed. Relations between the polarization of incident particles and that of scattered ones are presented, both in the full relativistic case and the nonrelativistic limit. The characteristic difference between the general and special cases lies in the backward direction: in the general cases the incident particles are simply bounced while in the special cases their polarization is turned over simultaneously. For pure Aharonov-Casher scattering there exist cases where the helicities of all scattered particles are reversed. This seems to be remarkable but appears unnoticed previously. Two mathematical approaches are employed to deal with the singularity of the electric and magnetic field and it turns out that the physical results are essentially the same.
The quantum-mechanical Aharonov-Bohm effect in the diffraction of charged particles by a toroidal solenoid containing a magnetic field is investigated. The total and differential elastic scattering cross sections depend on the magnetic flux inside the solenoid, even in the presence of a “black” ring-shaped screen which prevents charged particles from entering the region where the magnetic field is localized. Relations describing the momentum-transfer cross section for the elastic scattering of charged particles by a toroidal solenoid are obtained in the eikonal approximation and in a unitary model of scattering with a sharp jump in the partial amplitudes. The momentum-transfer scattering cross section is proportional to the average transfer of the longitudinal momentum of the scattered particle and can be expressed in terms of a force operator. It is shown that in the absence of a screen the momentum-transfer scattering cross section of toroidal solenoid is indeed determined only by the part of the incident beam that intersects the inner region of the toroidal solenoid, where the magnetic field intensity and, therefore, the Lorentz force are nonzero. At the same time, the momentum-transfer cross section for the scattering of charged particles by a toroidal solenoid covered by a “black” ring-shaped screen does not depend on the magnetic flux inside the solenoid and is identical to the momentum-transfer cross section for diffraction by the same screen. The contribution from scattering by an opening in the screen, which depends on the magnetic flux, is completely compensated by the contribution of the interference of the scattering amplitudes of the opening and the “black” screen.