Microscopic self dynamics in liquids: Connections between the Gaussian approximation and the asymptotic impulsive regime

In this paper we have studied the Gaussian approximation and its violation when applied to quantum fluids. Deviations from the Gaussian approximation, the so-called non-Gaussian effects, have been presented in a very general framework and subsequently compared to the final state effects, i.e. the differences between the exact single-particle response function and the well-known impulsive approximation. We have shown that, similarly to final state effects, non-Gaussian effects too can be expressed as a power series of the inverse momentum transfer, where the first two terms can be approximately calculated making use of equilibrium properties of the system. Finally, we have accomplished a practical test on experimentally measured non-Gaussian effects in liquid parahydrogen (at T=15.7 K and n=22.53 nm-3) by comparing them with the mentioned power series calculations. However, the agreement between the two data sets turned out to be rather poor, except for a general intensity level. The origin of this discrepancy is not evident at the moment and further tests on these physical quantities seem highly needed.