Cyclotron scattering lines in gamma-ray burst spectra

If cyclotron scattering, rather than absorption, is responsible for the line features observed recently in two gamma-ray burst spectra (Murakami et al., 1988), then the second and higher harmonics are due to resonant scattering events that excite the electron to Landau levels above the ground state. Here, relativistic Compton scattering cross sections are used to estimate the expected ratio of third to second harmonics in the presence of Doppler broadening. At the field strength (1.7 TG) required to give first and second harmonics at 19 keV and 38 keV, there should be no detectable third harmonic in the spectrum.