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.