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Abstract: The Gaussian approximation (GA) is widely employed in the description of single-molecule dynamics in liquids. In the GA framework it is assumed that the motion of particles is only determined by the time autocorrelation function of the particle velocity, in the whole wave-vector Q range of time- and space-dependent diffusive dynamics. Although often adopted, the validity of GA is not yet well assessed in different Q ranges, especially for the so-called quantum Boltzmann fluids. Liquid hydrogen, the most relevant test case for quantum dynamics simulation techniques, is also the canonical choice for experiments in self-dynamics, thanks to its ideal suitability to inelastic incoherent neutron scattering studies. Experimental evidence of the GA breakdown in hydrogen was recently achieved, but, to the best of our knowledge, the localization in Q space of non-Gaussian behavior was still undetermined, and no quantitative assessment has been obtained yet. These issues have been tackled and solved by a recent neutron investigation in conjunction with a quantum simulation of the velocity autocorrelation function. © 2011 American Physical Society.