Induced interactions in dilute atomic gases and liquid helium mixtures

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.