Kinetic energy and momentum distribution of isotopic liquid helium mixtures

TL;DR

This study uses quantum Monte Carlo simulations to analyze the momentum distribution and kinetic energy of helium isotopes in liquid mixtures at 2 K, revealing good agreement with experiments for some properties but notable discrepancies for He-3 kinetic energy at low concentrations.

Contribution

It provides a detailed quantum Monte Carlo analysis of helium isotope mixtures, including the role of Fermi statistics and the origin of kinetic energy measurement discrepancies.

Findings

Quantum statistics is negligible for He-3 below 20% concentration.

Good agreement with experiments for He-4 and pure He-3 energetics.

Discrepancy in He-3 kinetic energy likely due to underestimation of the tail in momentum distribution.

Abstract

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.