Scattering theory and the Aharonov--Bohm effect in quasiclassical
  physics
  Scattering of a nonrelativistic quantum-mechanical particle by an
impenetrable magnetic vortex is considered. The nonvanishing transverse size of
the vortex is taken into account, and the limit of short, as compared to this
size, wavelengths of the scattered particle is analyzed. We show that the
scattering Aharonov-Bohm effect persists in the quasiclassical limit owing to
the diffraction persisting in the short-wavelength limit. As a result, the
vortex flux serves as a gate for the propagation of short-wavelength, almost
classical, particles. This quasiclassical effect is more feasible to
experimental detection in the case when space outside the vortex is conical.
