A Microscopic Look at Liquid Helium: the 3He Impurity Case

TL;DR

This paper investigates the properties of a $^3$He impurity in liquid $^4$He at zero temperature using advanced many-body theories, accurately matching experimental spectra and revealing significant deviations from classical models.

Contribution

It demonstrates the effectiveness of the correlated basis function formalism in describing heavily correlated liquid helium systems, including detailed impurity excitation spectra and effective mass behavior.

Findings

Accurately reproduces experimental impurity spectra across momentum range.

Finds a ~50% increase in impurity effective mass at high momentum.

Shows deviations from quadratic Landau-Pomeranchuck behavior.

Abstract

The description of the properties of liquid Helium is a challenge for any microscopic many-body theory. In this context, we study the ground state and the excitation spectrum of one $^3$He impurity in liquid $^4$He at T=0 with the aim of illustrating the power of the correlated basis function formalism in describing heavily correlated systems. The strong interatomic interaction and the large density require the theory to be pushed to a high degree of sophistication. A many-body correlation operator containing explicit two- and thre-particle correlation functions is needed to obtain a realistic ground state wave function, whereas a perturbative expansion including up to two phonon correlated states must be enforced to study the impurity excitation energies. The theory describes accurately the experimental spectrum along all the available momentum range. As empirically shown by the experiments, a marked deviation from the quadratic Landau-Pomeranchuck behavior is found and the momentum dependent effective mass of the impurity increases of $\sim50~%$ at $q\sim1.7~\AA^{-1}$ with respect to its q=0 value. Although the main emphasis is given to the Correlated Basis Function theory, we present also comparisons with other methods, as diffusion Monte Carlo, variational Monte Carlo with shadow wave functions and time dependent correlations.