We show that the standard approach to the light scattering efficiency
fails in the case of electronic light scattering, The microscopic theo
ry is developed taking into account broadening of intermediate and fin
al states. The finite lifetime of the electronic excitations changes p
rincipally the theoretical analysis of the secondary radiation. Utiliz
ing examples of a three level system and a quantum well structure, we
predict the appearance of new characteristic features in the scatterin
g efficiency. The resonance profile for scattering from a doped quantu
m well shows a plateau with the width determined by the Fermi wavevect
or. This observation suggests a new method to evaluate the electron co
ncentration from optical measurements.