Theory of Neutron Scattering from Lattice Vibrations

TLDR: In this article, the theory of neutron scattering from lattice vibrations is redeveloped from the first principles and the expression for the scattering cross section contains factors depending on the anharmonicity explicitly, in addition to the conventional results and recent results based on the phonon Green function.

Abstract: The theory of neutron scattering from lattice vibrations is redeveloped from the first principles. The expression for the scattering cross section contains factors depending on the anharmonicity explicitly, in addition to the conventional results and recent results based on the phonon Green function. Near the Curie temperature T c of displacive-type ferroelectrics a certain term in the factors depends anomalously on temperature because of softening of frequencies and becomes comparable to or even greater than the conventional term. A similar deviation near the magnetic critical point in discussed briefly. A general theory of phonons at arbitrary temperature is also developed using the correlation function method which includes the ordinary phonon theory as the limiting case of the absolute zero, and the dispersion of the Cochran mode is determined. A self-consistent method of determining the frequency of a photon is proposed.