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We calculate the phase diagram for dilute mixtures of bosons and fermions at zero temperature. The linear stability conditions are derived and related to the effective boson-induced interaction between the fermions. We show that in equilibrium there are three possibilities: (a) a single uniform phase, (b) a purely fermionic phase coexisting with a purely bosonic one, and (c) a purely fermionic phase coexisting with a mixed phase.
Viverit et al. (2000) studied this question.