Calculation of the electron-proton scattering cross sections in a strongly magnetized plasma

We calculate and discuss the differential cross sections for nonrelativistic electrons in a strong magnetic field scattered by free protons with and without the emission of a photon. The electrons are assumed to be in the lowest Landau state before and after scattering. Forward scattering is the dominant part of the cross section but leads only to a small energy change per scattering. Another relevant contribution occurs if a cyclotron photon is emitted during the scattering event. This resonant process can change the electron energy by a large amount.