Inelastic Scattering of Thermal Neutrons from Liquid Helium

Abstract

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.

Static Structure Factor and Static Response Function of Superfluid Helium 4: a Comparative Analysis

“…Table 1 summarizes the experimental conditions; when absolute units are used, the corresponding calibration method is described. The work of Cowley and Woods [1] is the only one showing χ(q) explicitly (see Fig. 1b).…”

“…1b). Cowley and Woods [1] and Svensson et al [9] give directly S(q). Some other papers give S(q, ω) in absolute units, allowing a calculation of the zeroth moment S(q) and of χ(q) through (3); note that this gives more or less accurate lower bounds depending on the maximum energy transfer produced in the experiments.…”

“…The determination of χ(q) is more accurate than any positive moment because the factor 1/ω gives more weight to the one-phonon part, and reduces uncertainties due to the high energy tail of the multiphonon part. Figure 1, adapted from the pioneering work of Cowley and Woods [1], allows a comparison of the one phonon and multiphonon contribution to S(q) and χ(q)/n. It also shows that the one-phonon components are peaked around q = 20 nm −1 : the peak in S(q) (S pk ) reflects the short range order in the liquid, whereas the peak in χ(q)/n (χ pk /n) shows that the liquid is more susceptible to perturbations with this spatial period.…”

“…We have selected here those which give information about S(q), Z(q), and/or χ(q) and their pressure dependence, including neutron [1,[7][8][9][10][11] and X-ray [12][13][14] scattering data. Table 1 summarizes the experimental conditions; when absolute units are used, the corresponding calibration method is described.…”

“…This is particularly true when the pressure dependence is considered. In addition, χ(q) has been somewhat overlooked: there is only one published curve, obtained by Cowley and Woods in 1971 [1] at saturated vapor pressure (svp). This is puzzling when one thinks of the importance of χ(q) in density functional theory, where the static response can be used as an input [2,3] or a test [4,5] for the functional.…”