Asymmetries in the scattering of X-rays and neutrons by crystals

The theory of the scattering of x-rays and neutrons by an anharmonic crystal is discussed, with particular reference to the interference between the one-and two-phonon scattering. This interference gives rise to an extra contribution to the intensity of the scattered x-rays and to a change in both the intensity and the shape of the one-phonon part of the neutron scattering cross section. Detailed numerical calculations are performed for alkali halides. The results show that the asymmetries found recently in the scattering of x-rays by alkali halides are of this origin. In the case of neutron scattering the change in shape of the one-phonon peaks is so small that it is probably unobservable under experimental conditions available at present, but the change in the intensity should be observable.