Dynamic Many-Body Theory: The dynamics of atomic impurities in $^4$He

TL;DR

This paper develops microscopic many-body methods to study the dynamics of atomic impurities in superfluid helium-4, extending previous work to new impurity types and analyzing their interactions and effective masses.

Contribution

It introduces a detailed microscopic framework for impurity dynamics in helium-4, including new calculations for muonic helium-4, antiprotonic helium-4, and muonium atoms, with improved correlation function analysis.

Findings

Muonium probes short-range atomic interactions due to large zero-point motion.

Antiprotonic helium-4 has a negative chemical potential.

Effective masses of helium-3 and hydrogen atoms match experimental data.

Abstract

We implement manifestly microscopic many-body methods to study the dynamics of atomic impurities in a host quantum fluid, specifically $^4$He. Our investigations are motivated by experiments of muonium atoms within $^4$He with the goal of testing the universality of free fall by neutral bound states using unstable particles. Structure calculations are performed using standard semi-analytic methods; we extend here the calculations of our previos work (Journal of Low Temperature Physics {\bf 93}, 415-449 (1993)) to muonic \he4, antiprotonic \he4 and mounium atoms within \he4. We find that the muonium impurity probes, due to its large zero-point motion, the atomic interaction at rather short distances. Its chemical potential is estimated to be about 19 meV. Antiprotonic \he4 has, on the other hand, a negative chemical potential. Dynamics is treated by making all correlation functions time-dependent. In analogy to the derivation of the dynamics of the background liquid, we derive a working formula for the impurity self-energy that includes the most relevant physical effects. Results for the effective mass of \he3 and hydrogen atoms agree well with available experiments. The dispersion relations of muonic \he4 and antiprotonic \he4 pass through under the roton minimum.