Existing formulations for systems with complete translational invariance relate the dielectric function to the scattering probability in characteristic-energy-loss experiments. We have extended this relationship to the case of periodic systems. Energy-loss vs momentum-transfer measurements are of value because they provide a probe of the system for momentum transfer not accessible to optical measurements. Periodicity is shown to cause the formation of plasmon bands, and the possibility of long-lived higher-band plasmons is discussed. It is concluded that materials with a strong crystalline potential are the best candidates for such higher-band plasmons. The effect of the crystalline potential on the dispersion and damping of the lowest plasmon band, whose existence is well established experimentally, can also be obtained from the formulas that have been derived (which include the effects of local field).

• Received 5 September 1972

DOI:https://doi.org/10.1103/PhysRevB.7.2995