Dynamical theory of thermal neutron scattering. II.Pendellösungin inelastic peaks

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Abstract
A theory is presented in which the effect of the dynamical theory of diffraction on inelastic one-phonon peaks is taken into account to the first order in neutron-phonon interaction. In this theory, the distorted-wave Born approximation for the neutron-lattice Hamiltonian is used; the inelastic scattering amplitude for a phonon is then shown to be a coherent sum of the inelastic amplitudes due to all the plane-wave components of the Bloch waves that form the neutron wave function in the crystal under the stationary lattice condition. For this purpose, all the plane-wave components of the dynamical theory of the elastic scattering are on equal footing in determining the inelastic amplitude. The result is then a wavelength- and thickness-dependent structure in one-phonon peaks. An experimental configuration is suggested for observing Pendellösung effects in one-phonon peaks.