Kinetic energy of He atoms in liquid4He−3Hemixtures

Abstract

Deep inelastic neutron scattering measurements on liquid ${}^{3}\mathrm{He}{\ensuremath{-}}^{4}\mathrm{He}$ mixtures in the normal phase have been performed on the VESUVIO spectrometer at the ISIS pulsed neutron source at exchanged wave vectors of about $q\ensuremath{\simeq}120.0{\mathrm{\AA{}}}^{\ensuremath{-}1}.$ The neutron Compton profiles $J(y)$ of the mixtures were measured along the $T=1.96\mathrm{K}$ isotherm for ${}^{3}\mathrm{He}$ concentrations, x, ranging from 0.1 to 1.0 at saturated vapor pressures. Values of kinetic energies $〈T〉$ of ${}^{3}\mathrm{He}$ and ${}^{4}\mathrm{He}$ atoms as a function of x, $〈T〉(x),$ were extracted from the second moment of $J(y).$ The present determinations of $〈T〉(x)$ confirm previous experimental findings for both isotopes and, in the case of ${}^{3}\mathrm{He},$ a substantial disagreement with theory is found. In particular $〈T〉(x)$ for the ${}^{3}\mathrm{He}$ atoms is found to be independent of concentration yielding a value $〈T{〉}_{3}(x=0.1)\ensuremath{\simeq}12\mathrm{K},$ much lower than the value suggested by the most recent theoretical estimates of approximately 19 K.