Coherent quasielastic neutron scattering: A theorem about total neutron scattering functions for rotational jump diffusion of molecules on a lattice

We derive a theorem about the coherent quasielastic neutron-scattering signal from a lattice of N molecules that are undergoing rotational jump diffusion. If no correlations between the molecular jumps exist then the coherent quasielastic scattering signal is just N times that of a single molecule. The elastic contribution is just the diffraction diagram of the system. This implies, among others, that between the Brag peaks there is no coherent elastic contribution, i.e., between the Bragg peaks the coherent signal is purely quasielastic. These results for coherent scattering are in marked contrast to those in the case of incoherent scattering where one also can find elastic scattering outside the Bragg peaks.