The present work deals with the derivation of a neutron-scattering cross section for quasi-elastic scattering from a complex hydrogenous liquid. The internal motions of the proton within the molecule and possibly the motions of the protons between molecules have to be taken into account in a full description of the dynamical picture, and consequently also have to be included in the interpretation of scattered neutron spectra. The motion of the scattering protons is described as a superposition of the motion of the proton with respect of the center of gravity of the molecule on the motion of the center of gravity itself. A rapid jump motion of the proton during the time ${\tau }_1$ is considered; the origin of the jump might be an isomeric rotation or a change of proton position due to jumps in a hydrogen bond. In between the jumps, the proton is supposed to vibrate for a time ${\tau }_0$. The motion of the center of gravity of the molecule is supposed to be either a diffusive motion for a time ${{\tau }_1}^{\prime }$, if the molecule is free to move, or a vibration for a time ${{\tau }_0}^{\prime }$, if the molecule is bound, for instance via hydrogen bonds to neighbors.

• Received 8 April 1966

DOI:https://doi.org/10.1103/PhysRev.151.117