Diffracted x-ray transition radiation by a “half-bare” electron

The process of diffracted x-ray transition radiation by a high-energy "half-bare" electron in a crystalline target is considered in Bragg geometry. The electron is supposed to appear in the mentioned state, in which the field around it is significantly suppressed comparing to the equilibrium Coulomb one, in the result of preliminary penetration through an upstream amorphous target situated on some distance from the crystal. It is shown that the process of the electron's field regeneration after its exit from the upstream target dramatically modifies both the diffracted transition radiation angular distribution and its total yield making them dependent on the distance between the targets. Analytical expressions for these quantities, as well as their simple approximations, are derived. Almost arbitrary crystal orientation is considered. Special attention is drawn to the case of backward radiation geometry when the emitted radiation has to penetrate through the upstream target on its way to the detector.