Theory of neutron scattering from lattice vibrations, 2

A phonon theory developed previously which is a new approach besides the self consistent phonon theory and which is generalization of the Born phonon theory giving the rigorous phonon frequencies and normal coordinates of a crystal at an arbitrary temperature, is applied to neutron scattering from lattice vibrations in an anharmonic crystal. This application is done using a moment expansion of the canonical correlation function in the form of a continued fraction. A displacive ferroelectric and a perovskite crystal which exhibits a structural phase transition are discussed in some detail. A magnetic system having the spin-phonon interaction due to modulation of the exchange interaction caused by lattice vibrations is also discussed. A scattering cross section which depends explicitly upon the interaction acting on a phonon and has an anomalous temperature dependence near the transition point is found in some cases.