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

Induced interactions in dilute atomic gases and liquid helium mixtures