The excitation of electronic transverse energy levels in an intense magnetic field

Observations of the X-ray pulsar Hercules X-1 show a line emission feature at about 60 keV, which has been interpreted as the fundamental electron cyclotron line in a magnetic field of around six trillion gauss. In this interpretation, the line radiation results from transitions between transverse energy levels, which are quantized by the field. The expected line luminosity from the excitation of these levels by protons which are falling into the polar cap of a neutron star are calculated. They are assumed to attain kinetic energies up to around 200 MeV, the gravitational potential energy at the surface. The cross sections for high energy Coulomb encounters between small pitch angle protons and electrons in a strong field are measured and used to calculate the energy loss rate of the infalling protons. This rate, together with the rate of elastic nuclear proton collisions, is then used to calculate the number of line photons an infalling proton can be expected to produce, directly or indirectly. The results are applied to Hercules X-1.