Atomic Distribution in Liquid Helium by Neutron Diffraction

Abstract

The angular distribution of 1.04 A neutrons scattered by liquid helium has been measured for a series of temperatures between 1.6\ifmmode^\circ\else\textdegree\fi{}K and 5.04\ifmmode^\circ\else\textdegree\fi{}K over the angular range 3\ifmmode^\circ\else\textdegree\fi{} to 70\ifmmode^\circ\else\textdegree\fi{}. The scattering patterns are characterized by one principal maximum at an angle of 19.6\ifmmode\pm\else\textpm\fi{}0.5\ifmmode^\circ\else\textdegree\fi{} over a large range in liquid density. No marked change in the scattering pattern accompanies the $\ensuremath{\lambda}$ 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\ifmmode^\circ\else\textdegree\fi{}K, 4.24\ifmmode^\circ\else\textdegree\fi{}K, and in the region of 2\ifmmode^\circ\else\textdegree\fi{}K. The first maximum in the density is at ${3.5}_{0}$ A for the lowest temperature and at ${3.6}_{8}$ 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.