The scattering of neutrons by liquid helium has been studied over a wide range of wave-vector transfers, 0.2 < Q < 9.0 Å−1, and energy transfers [Formula: see text]. The measurements were performed with both a time-of-flight rotating crystal spectrometer and a triple-axis crystal spectrometer. The scattering at 1.1 °K showed a sharp one-phonon peak and a broad diffuse background. Measurements have been made of the energy and intensity of both components. At large wave-vector transfers the scattering is of the form expected from a system of almost free helium atoms. Measurements of the temperature dependence of the results at the smallest and largest wave vectors have been made. In the former case they show well-defined excitations above the λ point which are better defined for large wave vectors, while in the latter case they can be interpreted as giving evidence for the macroscopic occupation of the zero-momentum state. The results are compared with the available theoretical predictions.

The frequency/wave-vector dispersion relation for normal modes of vibration propagating along the [00ζ], [ζζ0], and [ζζζ] directions in uranium dioxide at 296 °K has been determined by studying the coherent one-phonon scattering of slow neutrons from a single-crystal specimen. Analysis of the results shows that a simple rigid-ion model of the crystal with axially symmetric forces between near-neighbor ions can provide qualitative agreement with experiment. A more complicated model, in which the ionic polarizabilities are taken into account, is needed to obtain quantitative agreement with the dispersion curves and with the known dielectric properties. Such a model provides an interpolation formula for computing the frequency distribution function and other related quantities, such as the Debye–Waller factors and lattice specific heat. Information concerning the anisotropy of the Debye–Waller factor for the oxygen ions and the configuration of the "magnetic" electrons in UO2 is derived by comparing these calculations with the appropriate experimental data. The optic-mode frequencies and dielectric constants of UO2 are shown to satisfy the Lyddane, Sachs, and Teller relation. The slopes of the acoustic-mode branches at small wave vectors are consistent with independently measured elastic constants.

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During the past decade there has been considerable progress in the study of the structure and elementary excitations of liquid helium. This has largely arisen from the development and refinement of neutron, x ray and light scattering techniques and also from more detailed ultrasonic measurements. A large part of this review is concerned with describing the results of these experiments and their implications for theories of liquid helium. During the last few years there has also been considerable progress made in the theory of the excitations in liquid helium. These developments are briefly reviewed and the most promising lines of development indicated.

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