Collapse transition in mixtures of Bosons and Fermions

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For mixtures of Bose and Fermi alkali atoms, the Fermion degrees of freedom can be integrated out in their finite temperature partition function. The final result can be expanded as a power series in the Boson density. Under appropriate conditions, the pairwise interaction between the bosons can be changed from positive to negative at a low enough temperature by the Fermion-mediated term and the Boson cloud may then collapse. For attractive Fermion-Boson interactions, there is also a collapse of the Fermion cloud. This transition is first order (discontinuous) because the leading order nonlinear interaction term between the Bosons is third order in Boson density with a negative coefficient. We discuss the finite temperature phase diagram of this transition. Our result may provide for an explanation of recent experimental observations by Modungo and coworkers.