Scattering of Low-Energy Electrons by Positive Ions in a Magnetic Field. I. Quantum Calculation of Transition Probabilities

Abstract

We analyze electron–ion collisions in a magnetic field at a low temperature, for which the electron’s Larmor radius is less than the characteristic impact parameter of close collisions without the magnetic field. This ratio of spatial scales is realized in the photospheres of magnetic white dwarfs and in the experiments of antihydrogen creation. Under considered conditions, an electron transits from the initial to the final state via an intermediate quasibound state. We put forward an approximate analytical procedure for the quantum-mechanical calculation of the probabilities for an electron to transit between Landau levels due to a collision with an ion. We reduce the calculation to the inversion of finite-dimension matrices.