In solid systems, distortions of the longitudinal nuclear-momentum distributions manifest themselves as departures from the Gaussian Approximation. These can be due to either the non-isotropic and/or non-harmonic nature of nuclear-momentum distributions, and these two effects are not easy to disentangle. As the harmonic Born Oppenheimer approximation (BOA) seems to account very well for crystal vibrations in LiH/ LiD at room temperature, a hypothesis can be put forward that ca. 2-3% of observed deviations compared to first-principles predictions should be mainly caused by collisionally induced non-BOA effects and associated anharmonicities. To test this hypothesis, LiH/LiD powders will be measured at temperatures T=10-500 K. Monte-Carlo fitting of these data will be used for a detailed comparison with predictions of harmonic and anharmonic ab initio calculations.