Raman scattering by longitudinal-optical phonons has been measured in
GaAs-AlAs multiple quantum wells at high magnetic fields. Doubly reson
ant scattering processes are observed at photon energies corresponding
to magneto-excitons with different principal quantum numbers for the
incoming and outgoing channels. The existence of these initially forbi
dden scattering processes, their resonance energies, and their relativ
e intensities are correctly reproduced by our theoretical description.
The model takes into account the excitonic nature of the intermediate
states, as well as scattering processes involving a nonzero in-plane
phonon wave vector, which is required to allow inter-landau level scat
tering of the exciton.