X-Ray Scattering from Liquid Helium

We have measured the liquid structure factor $S(k)$ for liquid He⁴ and for liquid He³ by x-ray diffraction. Our results for liquid He⁴ agree with the Feynman formula k2mc in the range $0.3<k<0.6$ ^-1, in contrast to previous measurements of $S(k)$ which fell about 25% below k2mc 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 He³ than for liquid He⁴, 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 He⁴ vapor at 4.2 K, 0.98 atm. For He⁴ vapor, $g(r)$ shows a distinct nearest-neighbor shell and probably a second-nearest-neighbor shell.