  The shakeup emission spectrum in a two-dimensional electron gas in a strong
magnetic field is calculated analytically. The case of a localized photocreated
hole is studied and the calculations are performed with a Nozieres-De
Dominicis-like Hamiltonian. The hole potential is assumed to be small compared
to the cyclotron energy and is therefore treated as a perturbation. Two
competing many-body effects, the shakeup of the electron gas in the optical
transition, and the excitonic effect, contribute to the shakeup satellite
intensities. It is shown, that the range of the hole potential essentially
influences the shakeup spectrum. For a short range interaction the above
mentioned competition is more important and results in the shakeup emission
quenching when electrons occupy only the lowest Landau level. When more than
one Landau level is filled, the intensities of the shakeup satellites change
with magnetic field nonmonotonically. If the interaction is long range, the
Fermi sea shakeup processes dominate. Then, the satellite intensities smoothly
decrease when the magnetic field increases and there is no suppression of the
shakeup spectrum when the only lowest Landau level is filled. It is shown also
that a strong hole localization is not a necessary condition for the SU
spectrum to be observed. If the hole localization length is not small compared
to the magnetic length, the SU spectrum still exists. Only the number of
contributions to the SU spectrum reduces and the shakeup processes are always
dominant.
