Breakdown of the Born approximation in Aharonov-Bohm scattering

J.-Q. Liang

M. Gomes, J. M. C. Malbouisson, A. J. da Silva

J.-Q. Liang, X. X. Ding

M. M. Panja, P K Bera, B. Talukdar

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.

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.