Collision frequency and Coulomb scattering in an intense magnetic field

In the enormous magnetic fields anticipated at the surface of neutron stars, the geometry of a scattering event involving charged particles is drastically altered. A number of familiar concepts, including the cross section, and collision frequency, are redefined in consequence following a one-dimensional multichannel approach. Separate collision frequencies are defined for each Landau level, displaying a strong oscillatory behavior as a function of the electron's energy. For electrons energetically confined in the lowest Landau orbital only backward-scattering events contribute to the collision frequency. New analytic expressions are obtained for the Coulomb matrix elements in the magnetic field. The results are used to study the effect of electron-ion scattering on the properties of electrons occupying low-lying Landau levels.