Kinetic energy and momentum distribution of isotopic liquid helium mixtures

The momentum distribution and atomic kinetic energy of the two isotopes of helium in a liquid mixture at temperature T=2 K are computed by quantum Monte Carlo simulations. Quantum statistics is fully included for He-4, whereas He-3 atoms are treated as distinguishable. Comparison of theoretical estimates with a collection of the most recent experimental measurements shows reasonable agreement for the energetics of He-4 and pure He-3. On the other hand, a significant discrepancy (already observed in previous works) is reported between computed and measured values of the He-3 kinetic energy in the mixture, in the limit of low He-3 concentration. We assess quantitatively the importance of Fermi statistics and find it to be negligible for a He-3 concentration less than approximately 20%. Our results for the momentum distributions lend support to what already hypothesized by other authors, namely that the discrepancy is likely due to underestimation of the He-3 kinetic energy contribution associated with the tail of the experimentally measured momentum distribution.