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Actually, both restrictions are always present because they are general. Whereas the energy conservation is easily covered by the emission of photons, the momentum conservation is overcome because of the uncertainty principle. Indeed, for a free charge carrier, the momentum has a finite value, but its positional coordinates are uncertain; that is, whereas the free charge carrier belongs to the whole crystal (i.e., it is delocalized over the whole crystal) the coordinates of the trapped charge carrier are pretty well-defined by the coordinates of the defects. In classical physics, this is equivalent to an inelastic collision of a charge carrier with a very massive body. Thus, the momentum of the trapped carrier is also elusive.
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