X-Ray Scattering from Liquid Helium

Abstract

We have measured the liquid structure factor $S(k)$ for liquid ${\mathrm{He}}^{4}$ and for liquid ${\mathrm{He}}^{3}$ by x-ray diffraction. Our results for liquid ${\mathrm{He}}^{4}$ agree with the Feynman formula $\frac{\ensuremath{\hbar}k}{2mc}$ in the range $0.3<k<0.6$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$, in contrast to previous measurements of $S(k)$ which fell about 25% below $\frac{\ensuremath{\hbar}k}{2mc}$ in this range. The peak in the pair distribution function $g(r)$ derived from the scattering data occurs at greater interatomic distance and is lower, broader, and less symmetrical for liquid ${\mathrm{He}}^{3}$ than for liquid ${\mathrm{He}}^{4}$, in agreement with predictions based on variational calculations. However, the experiments indicate slightly more structure in both liquids than the calculations predict. We have also measured $S(k)$ for ${\mathrm{He}}^{4}$ vapor at 4.2 K, 0.98 atm. For ${\mathrm{He}}^{4}$ vapor, $g(r)$ shows a distinct nearest-neighbor shell and probably a second-nearest-neighbor shell.