Atomic Distribution in Liquid Helium by Neutron Diffraction

The angular distribution of 1.04 A neutrons scattered by liquid helium has been measured for a series of temperatures between 1.6^∘{}K and 5.04^∘{}K over the angular range 3^∘{} to 70^∘{}. The scattering patterns are characterized by one principal maximum at an angle of 19.6±{}0.5^∘{} over a large range in liquid density. No marked change in the scattering pattern accompanies the λ transition. It is shown that for large-angle scattering the liquid behaves like a system of free helium atoms. Scattering intensities normalized to the differential cross section for a free helium atom have been transformed to give the radial distribution functions at 5.04^∘{}K, 4.24^∘{}K, and in the region of 2^∘{}K. The first maximum in the density is at 3.5₀ A for the lowest temperature and at 3.6₈ A for the highest. The density change is not accounted for by the shift of the maximum, and a decrease in the number of neighbors is postulated. The mean radial positions assigned to the first and second neighbors using the analysis of this paper agrees with a close-packed configuration of symmetrical particles, but the average number of first neighbors appears to be less than a complete close-packed arrangement, in keeping with the random arrangement expected for a liquid.