as panels (a),(b), respectively, except for $\chi_{bf}=10$. Plotted quantities are in normalized units.[]{data-label="fig1"}](fig1d.eps "fig:"){width="4.2cm" height="4.2cm"}

In Fig.\[fig1\]a we depict the bosonic and fermionic densities obtained with the self-consistent approach for a BFM with repulsive bosonic interactions ($\chi_{b}>0$) and attractive bosons fermion interaction ($\chi_{bf}<0$). We see that while the bosons remain confined in the middle of the trap, the fermionic density is quite extended in space and has a hump corresponding to the bosonic component. This hump originates from the contribution of the fermions trapped by the BEC acting on the fermions as a potential well (trapping impurity). Similar results were also reported in [@Karpiuk2].

An interesting problem which has not been investigated is the distribution of the bosonic and fermionic levels in their effective potentials. This is done in Fig. \[fig1\]b from which we see the presence of two fermionic levels formed below the parabola at the boottom of the Fermi sea. Notice that the effective potential seen by the fermions deviates from the original parabolic one only in the center of the trap due the presence of the potential well created by the bosonic density. Thus, the effective potential seen by the bosons is much deeper and wider, due 