×

Scattering of spin-polarized electron in an Aharonov-Bohm potential. (English) Zbl 1137.81373

Summary: The scattering of spin-polarized electrons in an Aharonov-Bohm vector potential is considered. We solve the Pauli equation in \(3 + 1\) dimensions taking into account explicitly the interaction between the three-dimensional spin magnetic moment of electron and magnetic field. Expressions for the scattering amplitude and the cross section are obtained for spin-polarized electron scattered off a flux tube of small radius. It is also shown that bound electron states cannot occur in this quantum system. The scattering problem for the model of a flux tube of zero radius in the Born approximation is briefly discussed.

MSC:

81U05 \(2\)-body potential quantum scattering theory
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Aharonov, Y.; Bohm, D., Phys. Rev., 115, 485 (1959)
[2] Peshkin, M.; Tonomura, A., The Aharonov-Bohm Effect (1989), Springer-Verlag: Springer-Verlag Berlin, For a review see
[3] Huang, K., Quarks, Leptons, and Gauge Fields (1982), World Scientific: World Scientific Singapore · Zbl 0997.81502
[4] Alford, M. G.; Wilczek, F., Phys. Rev. Lett., 62, 1071 (1989)
[5] Khalilov, V. R., Phys. Rev., A71, 012105 (2005)
[6] Hagen, C. R., Phys. Rev. Lett., 64, 503 (1990)
[7] S.P. Gavrilov, D.M. Gitman, J.L. Tomazelli, e-print archive: hep-th/0701062v1; S.P. Gavrilov, D.M. Gitman, J.L. Tomazelli, e-print archive: hep-th/0701062v1
[8] Khalilov, V. R., Mod. Phys. Lett., A21, 1647 (2006)
[9] Landau, L. D.; Lifshitz, E. M., Quantum Mechanics (1977), Pergamon: Pergamon New York · Zbl 0081.22207
[10] Gradshteyn, I. S.; Ryzhik, I. M., Table of Integrals, Series, and Products (1994), Academic Press: Academic Press San Diego · Zbl 0918.65002
[11] Flügge, S., Practical Quantum Mechanics 2 (1971), Springer-Verlag: Springer-Verlag Berlin-Heidelberg-New York · Zbl 1400.81003
[12] Khalilov, V. R.; Ho, C. L., Mod. Phys. Lett., A13, 615 (1999)
[13] Aharonov, Y.; Casher, A., Phys. Rev. Lett., 53, 319 (1984)
[14] He, X.-G.; McKellar, B. H.J., Phys. Lett., B256, 250 (1990)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.