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Physical Review B

Condensate fraction and atomic kinetic energy of liquid He3−He4 mixtures

Souleymane Diallo, Jonathan V Pearce, R. T. Azuah, F. Albergamo, H. R. Glyde

Published Oct 5, 2006• 10 citations
Publisher

Abstract

We present neutron-scattering measurements of the momentum distribution of liquid $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ mixtures. The experiments were performed at wave vectors $Q$, $26\ensuremath{\leqslant}Q\ensuremath{\leqslant}29\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{\ensuremath{-}1}$, 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 ${n}_{0}=(7.25\ifmmode\pm\else\textpm\fi{}0.75)%$ at $x=0$ to $(11\ifmmode\pm\else\textpm\fi{}3)%$ at $x=15--20\phantom{\rule{0.2em}{0ex}}%$. 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, $n(\mathbf{k})$. Rather an $n(\mathbf{k})$ 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 $n(\mathbf{k})$ is consistent with calculated $n(\mathbf{k})$. Thus agreement between theory and experiment is obtained comparing $n(\mathbf{k})$ in contrast to earlier findings based on comparing calculated and observed $^{3}\mathrm{He}$ kinetic energies.

DOI
10.1103/physrevb.74.144503

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