Condensate fraction and atomic kinetic energy of liquid {sup 3}He-{sup 4}He mixtures

We present neutron-scattering measurements of the momentum distribution of liquid {sup 3}He-{sup 4}He mixtures. The experiments were performed at wave vectors Q, 26{<=}Q{<=}29 A {sup -1}, on the MARI time-of-flight spectrometer at the ISIS Facility, Rutherford Appleton Laboratory, a spallation neutron source. Mixtures with {sup 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{sub 0} and the momentum distributions of {sup 3}He and {sup 4}He atoms. We find that n{sub 0} increases somewhat above the pure {sup 4}He value when {sup 3}He is added; e.g., from n{sub 0}=(7.25{+-}0.75)% at x=0 to (11{+-}3)% at x=15-20 %. This agrees with predictions but is less than the only previous measurement. We find a {sup 4}He kinetic energy K{sub 4} for pure {sup 4}He that agrees with previous determinations. K{sub 4} decreases somewhat with increasing {sup 3}He concentration, less than observed previously and found in early calculations but in agreement with a more recent Monte Carlo calculation. The {sup 3}He response is not well reproduced by a Fermi-gas momentum distribution, n(k). Rather an n(k) having a small step height at the Fermi surface and a substantial high-momentummore » tail characteristic of a strongly interacting Fermi liquid provides a good fit. This n(k) is consistent with calculated n(k). Thus agreement between theory and experiment is obtained comparing n(k) in contrast to earlier findings based on comparing calculated and observed {sup 3}He kinetic energies.« less