The theory of incoherent nuclear resonant scattering of synchrotron radiation accompanied by absorption or emission of phonons in a crystal lattice is developed. The theory is based on the Maxwells equations and time-dependent quantum mechanics under the condition of incoherent scattering of radiation by various nuclei. A concept of coherence in scattering processes, properties of the synchrotron radiation, and conditions of measurement are discussed. We show that employing the monochromator with a narrow bandwidth plays a decisive role.
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