Collapse transition in mixtures of Bosons and Fermions
  For mixtures of Bose and Fermi alkali atoms, the Fermion degrees of freedom can be integrated out in their {\bf 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 {\bf 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. 
S. T. Chui and V. N. Ryzhov