The Aharonov-Bohm effect in scattering of nonrelativistic electrons by a   penetrable magnetic vortex
  Quantum-mechanical theory for scattering of nonrelativistic charged particles with spin by a penetrable magnetic vortex is elaborated. The scattering differential cross section is shown to consist of two terms, one describing diffraction on the vortex in the forward direction and another one describing penetration through the vortex. The Aharonov-Bohm effect is manifested as a fringe shift in the diffraction pattern. The penetration effect is analyzed for the case of the uniform distribution of the magnetic field strength inside the vortex. We find that the penetrability of the magnetic vortex does not affect the diffraction pattern, and, hence, the Aharonov-Bohm effect is the same for a penetrable vortex as for an impenetrable one. 
Yurii A. Sitenko
quant-ph hep-th math-ph math.MP physics.ins-det