Neutron-diffraction study of the static structure factor and pair correlations in liquidHe4

An investigation of the structure of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at saturated vapor pressure by means of neutron diffraction is reported for 11 temperatures in the range 1.00 to 4.27 K. At each temperature, the static structure factor $S\left(Q\right)\mathrm{}$ is obtained for $0.8\le Q\le 10.8$ ${\mathrm{\AA }}^{-1\mathrm{}}$ with an average statistical precision of 0.8% and with a residual systematic error which is estimated to be <1%. Our results for $S\left(Q\right)\mathrm{}$ are in good agreement with the very precise x-ray results of Hallock which cover the range $0.133\le Q\le 1.125$ ${\mathrm{\AA }}^{-1\mathrm{}}$ and with the requirement that the corresponding pair correlation functions $g\left(r\right)\mathrm{}$, which we obtain from $S\left(Q\right)\mathrm{}$ by Fourier inversion, vanish inside the core of the interatomic potential. The temperature variations of both $S\left(Q\right)\mathrm{}$ and $g\left(r\right)\mathrm{}$ show clearly that the degree of spatial order in liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ increases with decreasing temperature above the $\lambda$ point, 2.17 K, but then decreases with decreasing temperature in the superfluid phase. The latter behavior is believed to be a consequence of the Bose-Einstein condensation. A comparison of our results for $S\left(Q\right)\mathrm{}$ and $g\left(r\right)\mathrm{}$ at 1.00 K with the results of theoretical calculations for $T=0\mathrm{}$ reveals significant discrepancies which indicate that there is a greater degree of spatial order in liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ than would be the case if the atoms interacted via additive forces of the Lennard-Jones type.