Scattering of electrons off hollow cylindrical potentials

We study the scattering of a beam of electrons that is incident along the transverse direction on a hollow cylindrical potential. Solutions in closed forms are obtained for the case where the incident beam is a plane wave and also for the case of an arbitrary wave packet. The scattering cross-section that appears as an infinite sum over partial waves corresponding to different azimuthal quantum number is shown to converge rapidly, so that for all practical applications only the first few terms would suffice. It is found that at certain specific energies that correspond to the bound states of the cylindrical potential, the scattering cross-section vanishes. Angular distribution of the scattered flux for plane wave incidence is also studied and it shows interesting signatures of confinement. , Copyright © 2010 American Scientific Publishers.