In the present paper we investigate coherent bremsstrahlung of high energy electrons moving in a periodically deformed single crystal with a complex base. The formula for corresponding differential cross-section is derived for an arbitrary deformation field. The conditions are discussed under which the influence of the deformation is important. The case is considered in detail when the electron enters into the crystal at small angles with respect to a crystallographic axis. It is shown that in dependence of the parameters, the presence of the deformation can either enhance or reduce the bremsstrahlung cross-section.
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