Kinetic energy of He atoms in liquid ${}^4$He-${}^3$He mixtures

Deep Inelastic Neutron Scattering measurements on liquid ${}^3$He-${}^4$He mixtures in the normal phase have been performed on the VESUVIO spectrometer at the ISIS pulsed neutron source at exchanged wavevectors of about $q \simeq 120.0$\mathring{A}$^{-1}$. The neutron Compton profiles J(y) of the mixtures were measured along the $T=1.96$ K isotherm for ${}^3$He concentrations, $x$, ranging from 0.1 to 1.0 at saturated vapour pressures. Values of kinetic energies, $<T>$, of ${}^3$He and ${}^4$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 ${}^3$He, a substantial disagreement with theory is found. In particular $<T (x)$forthe$^3$He atoms is found to be independent of concentration yielding a value $<T{>}_3(x=0.1)\simeq 12K$, much lower than the value suggested by the most recent theoretical estimates of approximately 19 K .