A Theoretical Approach to Dynamical Diffraction of X-rays in the Bragg Case with the Green’s Function Method

The dynamical diffraction theory of X-rays for a distorted crystal with the Green’s function method is applied to the Bragg case. The transmitted and diffracted crystal waves are represented as the solutions of the integral equations using the Green’s function. For a perfect crystal, the most exact form of the solution of the equations is given by the Green's function and its derivatives, and the waves are analytically expressed by using them. The results can be applied in a general case where the amplitude modulation of the incident wave is not negligibly small compared with the wave vector. If the amplitude modulation is small, those results are reduced essentially to the same as those given by Takagi’s theory