Coherent quasielastic neutron scattering and correlations between rotational jumps of molecules on a periodic lattice

We previously [Coddens, Phys. Rev. 63, 064105 (2001)] derived a theorem about the coherent quasielastic neutron-scattering signal from a d-dimensional lattice of N molecules that are undergoing rotational jump diffusion (around an n-fold axis), assuming that there are no correlations between the molecules. In the present paper molecular correlations are treated, but only in the sense that several molecules could reorient simultaneously as in a cog-wheel mechanism. Moreover, we do not examine the possibility that the relaxation times of these combined reorientations could depend on details of the local environment created by the neighbouring molecules. Finally also an ergodicity condition has to be fulfilled. Admitting for all these assumptions we can show that the correlations do not affect the coherent quasielastic scattering pattern in the following sense: The functions of Q that intervene in the description of the intensities remain unaltered, while the functions of omega can undergo a renormalization of the time scales. The latter changes cannot be detected as the time scales that would occur if the dynamics were independent are not available for comparison. In other words: Coherent quasielastic neutron scattering is not able to betray the existence of correlations of the restricted type that occur in our model. The assumptions that underly the model we present were made to allow a mathematically rigorous calculation of the scattering function. Other, perhaps more realistic cases may entail correlations of a type that is too difficult to be treated rigorously with our method of calculation. But our result presents an important non-trivial counter example to show that the absence of a clue for the presence of correlations in the data is not a sufficient criterium to conclude that such correlations are indeed absent.