Stability of Bose system in Bose – Fermi mixture with attraction between bosons and fermions

An effective Hamiltonian for the Bose system in the mixture of ultracold atomic clouds of bosons and fermions is obtained by integrating out the Fermi degrees of freedom. An instability of the Bose system is found in the case of attractive interaction between components in good agreement with the experiment on the bosonic $^{87}$Rb and fermionic $^{40}$K mixture.