Collisional excitation of electron Landau levels in strong magnetic fields

The cross sections for excitation and deexcitation of the quantized transverse energy levels of an electron in a magnetic field are calculated for electron-proton and electron-electron collisions. Both the electron and proton are treated as free point charges moving at arbitrary velocities. These cross sections are of particular interest in studies of magnetic neutron stars where a magnetic field of 10¹¹-10¹³ gauss and temperatures in excess of 10⁸ K are expected. The cross sections are calculated for arbitrary initial and final states; however, the discussion emphasizes excitations of ground-state electrons (the dominant process in accreting neutron stars). Our results for electronproton excitations show that proton recoil, which was neglected in previous calculations, and relativistic corrections may both be important. We also present the first calculation of the cross section for electron-electron excitations, and show that this process may contribute 10-20% of the excitation rate from electron-proton scattering in a Maxwellian plasma. Finally, we calculate the cross section for electron-proton small-angle scattering. The resulting relaxation rates for the electron velocity distribution are modified by the magnetic field and the value of the Coulomb logarithm may be significantly increased due to the quantization of the transverse energy levels of the proton.