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 ⁴He, whereas ³He 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 ⁴He and pure ³He. On the other hand, a significant discrepancy (already observed in previous studies) is reported between computed and measured values of the ³He kinetic energy in the mixture, especially in the limit of low ³He concentration. We assess quantitatively the importance of Fermi statistics and find it to be negligible for a ³He concentration ≲20%. Our results for the momentum distribution lend support to what was already hypothesized by other authors, namely, that the discrepancy is likely due to underestimation of the ³He kinetic energy contribution associated with the tail of the experimentally measured momentum distribution.