Line shifts in electron planar channeling radiation from lattice vibrations

A density matrix formulation of the dynamical theory of spectral shifts from lattice vibrations in electron planar channeled radiation is presented. For the two-level bound systems associated with lower energy channeling, positive shifts can be demonstrated. In the case of higher-energy channeling where the bound system is multi-level, reduced positive shifts and negative shifts are shown. The theory suggests a novel method for experimentally determining a transverse, vibration correlation length in crystals