Kinetic energy and momentum distribution of isotopic liquid helium mixtures

摘要

The momentum distribution and atomic kinetic energy of the two isotopes ofhelium in a liquid mixture at temperature T=2 K are computed by quantum MonteCarlo simulations. Quantum statistics is fully included for He-4, whereas He-3atoms are treated as distinguishable. Comparison of theoretical estimates witha collection of the most recent experimental measurements shows reasonableagreement for the energetics of He-4 and pure He-3. On the other hand, asignificant discrepancy (already observed in previous works) is reportedbetween 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 importanceof Fermi statistics and find it to be negligible for a He-3 concentration lessthan approximately 20%. Our results for the momentum distributions lend supportto what already hypothesized by other authors, namely that the discrepancy islikely due to underestimation of the He-3 kinetic energy contributionassociated with the tail of the experimentally measured momentum distribution.