Critical temperature of Bose Einstein condensation in trapped atomic Bose Fermi mixtures

We calculate the shift in the critical temperature of Bose–Einstein condensation for a dilute Bose–Fermi mixture confined by a harmonic potential, to lowest order in both the Bose–Bose and Bose–Fermi coupling constants. The relative importance of the effect on the critical temperature of the boson–boson and boson–fermion interactions is investigated as a function of the parameters of the mixture. The possible relevance of the shift of the transition temperature in current experiments on trapped Bose–Fermi mixtures is discussed.