  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 Maxwell's 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.
