Solution of the X-ray edge problem for 2D electrons in a magnetic field

The absorption and emission spectra of transitions between a localized level and a two-dimensional electron gas, subjected to a weak magnetic field, are calculated analytically. Adopting the Landau level bosonization technique developed in previous papers, we find an exact expression for the relative intensities of spectral lines. Their envelope function, governed by the interaction between the electron gas and the core hole, is reminescent of the famous Fermi edge singularity, which is recovered in the limit of a vanishing magnetic field.