Application of the invariance principle in the dynamic theory of X-ray scattering

The invariance principle of Ambarsumian is applied to the solution of X-ray diffraction problem in single crystals in the symmetric Bragg case. A quadratic equation with respect to the reflection coefficient rho is obtained for a semi-infinite crystal. Evident expressions for the reflection coefficient rho/sub n/ and transmission coefficient Q/sub n/ are found by establishing relations between the solution of the diffraction problem in the crystal with a finite number n of reflecting planes and that of the diffraction problem in a semi-infinite one. The formulas obtained may be applied to any periodically layered medium. (author)