Induced interactions in dilute atomic gases and liquid helium mixtures

TL;DR

This paper derives general expressions for induced interactions in dilute atomic gas mixtures, highlighting their implications for understanding $^3$He in liquid $^4$He, applicable to both fermionic and bosonic systems.

Contribution

It provides a unified thermodynamic framework to calculate induced interactions in dilute mixtures for arbitrary interaction strengths.

Findings

Derived expressions for induced interactions in fermionic and bosonic mixtures.

Discussed implications for $^3$He-$^4$He liquid solutions.

Applicable to arbitrary interaction strengths.

Abstract

In dilute mixtures of two atomic gases, interactions between two minority atoms acquire a contribution due to interaction with the majority component. Using thermodynamic arguments, we derive expressions for this induced interaction for both fermions and bosons for arbitrary strength of the interaction between the two components. Implications of the work for the theory of dilute solutions of $^3$He in liquid $^4$He are discussed.