High-Energy Neutron Scattering Measurements on Liquid Helium and Bose Condensation in He II

Differential neutron scattering cross sections for liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ have been obtained for momentum transfers along the free-particle excitation curve up to 20.3 ${\mathrm{\AA }}^{-1\mathrm{}}$. Momentum transfers in this range are much higher than in previously reported work. The measured recoil energies as well as the angular dependence of the scattering confirm that the neutron scattering, at these high values of $\kappa$, is sensitive to the motions of single helium atoms. A temperature dependence in the widths of the cross-section peaks, as well as shape changes in these peaks as the temperature is decreased below $T_{\lambda }$ is consistent with the idea that a narrow condensate component contributes to the scattering for $T<\mathrm{}{T}_{\lambda }$. Results from a detailed comparison of the measured cross sections with a theory for high-energy neutron scattering are reported. The kinetic energy per liquid-helium atom is deduced from this theory-experiment comparison and is found to be in agreement with computations of the kinetic energy based on thermodynamic phase equilibria considerations. A fractional occupation of the zero-momentum condensate state of (8.8 ± 1.3)% at 1.27 °K is also deduced from this theory-experiment comparison.