Comments on charged particle scattering in the presence of a quantising magnetic field

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Abstract
Transition probabilities and scattering cross sections are derived for charged particle potential scattering in the presence of a quantising constant magnetic field. They are derived within the S-matrix and the Green's function approaches and found to differ significantly from the ones defined for spherical geometries. Three types of scattering potential are considered: screened Coulombic, pure Coulombic and exponential. For all of them the first-order matrix elements and accordingly, the transition probabilities and the cross sections are exactly calculated and given in analytic closed form. The optical theorem is derived, with the result that the total scattering cross section is found to be expressed through the real part of the elastic scattering amplitude. The transition probabilities and the scattering cross sections are found to have singularities and accordingly to exhibit giant growth (cyclotron resonances) at values of the incident particle energy (along the z axis) exactly matching the energy differences between the initial and the final state Landau levels.