hump in the fermionic density and that excited states, although lowering their energies, remain almost equally spaced (this is due to the fact that the effective potential created by the fermions, except for the hump in the middle, looks still parabolic).

It is remarkable that this situation remains stable under time evolution, as one can see from the left panel of Fig. \[fig2\]. In Fig. \[fig1\]c, we show the situation for repulsive Bose-Fermi interactions ($\chi_{bf}>0$). From Fig. \[fig1\]c we see that in this case fermions are expelled from (instead of attracted to) the region where bosons are spatially concentrated, this increasing their kinetic energy and rising a pressure on the condensate. Also notice from Fig. \[fig1\]d that the corresponding energy levels are shifted up in energy, much more for bosons (which have an effective potential very deformed at the bottom) than for the fermions (which see almost the original parabolic trap but with a narrow hump in the middle). From this figure it is clear that the case of repulsive interactions ($\chi_{bf}>0$) is also of interest because, although not producing trapping states, it induces correlations among the fermions as is evident from the deviations from equally spaced levels observed in 