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

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, 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 not through the imaginary part of the elastic scattering amplitude but through the real part. The analytic structure of the elastic scattering series in the presence of the magnetic field is found to resemble the scattering series when particles with internal discrete structure collide. (author)