{
  "id": "cond-mat/0609529",
  "version": "v1",
  "published": "2006-09-20T21:59:26.000Z",
  "updated": "2006-09-20T21:59:26.000Z",
  "title": "Bose-Einstein Condensation and Kinetic energy of liquid $^3$He-$^4$He Mixtures",
  "authors": [
    "S. O. Diallo",
    "J. V. Pearce",
    "R. T. Azuah",
    "F. Albergamo",
    "H. R. Glyde"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.supr-con"
  ],
  "abstract": "We present neutron scattering measurements of the momentum distribution of liquid ${^3}$He-${^4}$He mixtures. The experiments were performed at wavevectors $Q$, 26 $\\leq$ $Q$ $\\leq$ 29 {\\AA$^{-1}$}, on the MARI time-of-flight spectrometer at the ISIS Facility, Rutherford Appleton Laboratory, a spallation neutron source. Mixtures with $^3$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 $^3$He and $^4$He atoms. We find that $n_0$ increases somewhat above the pure $^4$He value when $^3$He is added; e.g from $n_0=(7.25\\pm0.75)%$ at $x=$ 0 to $(11\\pm3)%$ at $x=$ 15-20%. This agrees with predictions but is less than the only previous measurement. We find a $^4$He kinetic energy $K_4$ for pure $^4$He that agrees with previous determinations. $K_4$ decreases somewhat with increasing $^3$He concentration, less than observed previously and found in early calculations but in agreement with a more recent Monte Carlo calculation. The $^3$He response is not well reproduced by a Fermi gas momentum distribution, $n(\\bf{k})$. Rather an $n(\\bf{k})$ 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 $n(\\bf{k})$ is consistent with calculated $n(\\bf{k})$. Thus agreement between theory and experiment is obtained comparing $n(\\bf{k})$ in contrast to earlier findings based on comparing calculated and observed $^3$He kinetic energies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-20T21:59:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kinetic energy",
      "bose-einstein condensation",
      "substantial high momentum tail characteristic",
      "fermi gas momentum distribution",
      "bose-einstein condensate fraction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006cond.mat..9529D"
    }
  }
}