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

TL;DR

This paper proves that under certain assumptions, coherent quasielastic neutron scattering cannot detect specific types of molecular correlations during rotational jumps on a lattice, as correlations only renormalize time scales without altering observable patterns.

Contribution

The paper extends a previous theorem to include molecular correlations in rotational jump diffusion, showing these correlations do not affect the scattering pattern except for renormalized time scales.

Findings

Correlations do not alter the Q-dependent functions in the scattering pattern.

Time scales in the scattering functions are renormalized by correlations.

Coherent quasielastic neutron scattering cannot detect certain molecular correlations.

Abstract

We previously derived a theorem about the {\em 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.