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

Method of functional integration in the problem of line width of parametric X-ray relativistic electron radiation in a crystal

“…Experimental studies of PXR line widths have shown [5] that the line widths were, however, much larger than the natural PXR line width. Performed analysis of experimental data in [5,6] is shown that the multiple scattering must make considerable influence on line width of PXR.…”

“…In [6] a theory of the line width of "backward" PXR based on the method of functional integration was suggested. On the basis of this theory in [6] the simplest case of the multiple scattering effect on the PXR spectral-angular characteristics was considered in which multiple scattering was studied only in continuous field of the crystal atomic strings. This paper is devoted to investigation of non-coherent multiple scattering effect of particles on the line width in a crystal.…”

“…This paper is devoted to investigation of non-coherent multiple scattering effect of particles on the line width in a crystal. Offered averaging method in [6] over PXR spectral-angular density is generalized to the case, when coherent and non-coherent effects in particle multiple scattering on atomic strings are took into account. It is shown that this problem in many respects is similar to the problem of the Landau-Pomeranchuk-Migdal effect of multiple scattering on coherent bremsstrahlung of high energy electrons in a crystal and in an amorphous medium [1,7,8,9,10].…”

“…Narrow lines then appear in the spectral-angular radiation density caused by particle field reflection from the crystallographic planes of atoms oriented transversely to z-axis on equal distance a from each other. Spectralangular radiation density corresponding to the line width frequency ω n is given by the equation [6]…”

“…Obtaining (1) it was supposed that the medium permittivity is close to unity and also photon absorption was neglected. The finite size of crystal leads us, as is well [5,6], to the natural line width of PXR. Small deviations of electron trajectory in crystal from linear one is caused by both particle plane channeling effect and multiple scattering on non-uniformities of lattice potential.…”