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 magneti c field, are calculated analytically. Adopting the Landau level bosoni zation technique developed in previous papers, we find an exact expres sion for the relative intensities of spectral lines. Their envelope fu nction, governed by the interaction between the electron gas and the c ore hole, is reminiscent of the famous Fermi edge singularity, which i s recovered in the limit of a vanishing magnetic field.