We propose a simple and accurate model for the electron static structure factors ͑and corresponding paircorrelation functions͒ of the three-dimensional unpolarized homogeneous electron gas. Our spin-resolved paircorrelation function is built up with a combination of analytic constraints and fitting procedures to quantum Monte Carlo data, and, in comparison to previous attempts, ͑i͒ fulfills more known integral and differential properties of the exact pair-correlation function, ͑ii͒ is analytic both in real and in reciprocal space, and ͑iii͒ accurately interpolates the newest, extensive diffusion-Monte Carlo data of Ortiz, Harris, and Ballone ͓Phys. Rev. Lett. 82, 5317 ͑1999͔͒. This can be of interest for the study of electron correlations of real materials and for the construction of new exchange and correlation energy density functionals.

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We present incoherent quasielastic neutron scattering measurements on ice Ih (ordinary ice) and Ic (cubic ice) which show the existence of nonharmonic motion of hydrogen at low temperatures, down to 5 K. We show that this dynamics is localized, nonvibrational, and related to the hydrogen disorder since it is absent in ordered ice VIII. A main jump distance of 0.75 A is identified, hence close to the distance between the two possible proton sites along the oxygen-oxygen bond. The dynamics is non-Arrhenius, has a large time rate of 2.7x10(11) s-1, and affects only a few percent of the total number of hydrogen atoms in the crystal. These results give evidence for the existence of concerted proton tunneling in these ice phases.

A high resolution (1.5 meV) inelastic neutron scattering experiment was carried out, aiming at an accurate investigation of the high frequency and low momentum dynamic response in heavy water. The experimental data confirm the existence of a dispersionless mode, besides the ordinary longitudinal collective dynamics. A simplified model, based on the interaction of two vibrational branches, is proposed to interpret the observed features of the dynamic spectra. The validity extent of this scheme is proved by applying it to room temperature neutron and x-ray data, to temperature and pressure dependent x-ray data, and to room temperature neutron data of vibrational density of states. The overall successfull results provided by this model, in conjunction with the combined analysis of the x-ray and neutron data on collective dynamics, enable a deeper insight into the complex mechanisms of the water dynamics and provide a simple phenomenological explanation for the transition from ordinary to fast sound.

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