Multiple scattering effect on the line width of parametric X-ray relativistic electron radiation in a crystal

It is shown that multiple scattering is of significant importance in the formation of the line width of parametric X-ray «backward» radiation of relativistic electrons in a crystal. A theory of the line width of this radiation based on the functional integration method is suggested. The problem of multiple scattering effects on parametric X-ray radiation is shown to be similar to the problem of the Landau–Pomeranchuk–Migdal multiple scattering effect on the bremsstrahlung of high-energy electrons in an amorphous medium.