We present neutron-scattering measurements of the momentum distribution of liquid ${}^3\mathrm{He}\text{−}{}^4\mathrm{He}$ mixtures. The experiments were performed at wave vectors $Q$, $26⩽Q⩽29{\mathrm{\AA }}^{-1}$, on the MARI time-of-flight spectrometer at the ISIS Facility, Rutherford Appleton Laboratory, a spallation neutron source. Mixtures with ${}^3\mathrm{He}$ concentrations $x$ between 0 and 20% were investigated both in the superfluid and normal phases. From the data, we extract the Bose-Einstein condensate fraction $n_0$ and the momentum distributions of ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ atoms. We find that $n_0$ increases somewhat above the pure ${}^4\mathrm{He}$ value when ${}^3\mathrm{He}$ is added; e.g., from $n_0=(7.25\pm 0.75)\%$ at $x=0$ to $(11\pm 3)\%$ at $x=15–20\%$. This agrees with predictions but is less than the only previous measurement. We find a ${}^4\mathrm{He}$ kinetic energy $K_4$ for pure ${}^4\mathrm{He}$ that agrees with previous determinations. $K_4$ decreases somewhat with increasing ${}^3\mathrm{He}$ concentration, less than observed previously and found in early calculations but in agreement with a more recent Monte Carlo calculation. The ${}^3\mathrm{He}$ response is not well reproduced by a Fermi-gas momentum distribution, $n\left(\mathbf{k}\right)$. Rather an $n\left(\mathbf{k}\right)$ having a small step height at the Fermi surface and a substantial high-momentum tail characteristic of a strongly interacting Fermi liquid provides a good fit. This $n\left(\mathbf{k}\right)$ is consistent with calculated $n\left(\mathbf{k}\right)$. Thus agreement between theory and experiment is obtained comparing $n\left(\mathbf{k}\right)$ in contrast to earlier findings based on comparing calculated and observed ${}^3\mathrm{He}$ kinetic energies.

• Received 21 February 2006

DOI:https://doi.org/10.1103/PhysRevB.74.144503