of the Bose (open circles and dotted line) Fermi (filled circles and continuous line) mixture with densities given in panel(a) (horizontal line refers to the Fermi level). Panels (c) and (d) are the same as panels (a),(b), respectively, except for $\chi_{bf}=10$. Plotted quantities are in normalized units.[]{data-label="fig1"}](fig1b.eps "fig:"){width="4.2cm" height="4.2cm"}

![(a). Fermionic and bosonic densities for the case of $\chi_{b}=1, \chi_{bf}=-10$, $N_f=20$ and normalized number of bosons $N_b=1$, for a parabolic trap of strength $\varepsilon=0.0025$ centered at $x_0=L/2=20\pi$. (b) Effective potentials and energy levels of the Bose (open circles and dotted line) Fermi (filled circles and continuous line) mixture with densities given in panel(a) (horizontal line refers to the Fermi level). Panels (c) and (d) are the same as panels (a),(b), respectively, except for $\chi_{bf}=10$. Plotted quantities are in normalized units.[]{data-label="fig1"}](fig1c.eps "fig:"){width="4.2cm" height="4.2cm"} ![(a). Fermionic and bosonic densities for the case of $\chi_{b}=1, \chi_{bf}=-10$, $N_f=20$ and normalized number of bosons $N_b=1$, for a parabolic trap of strength $\varepsilon=0.0025$ centered at $x_0=L/2=20\pi$. (b) Effective potentials and energy levels of the Bose (open circles and dotted line) Fermi (filled circles and continuous line) mixture with densities given in panel(a) (horizontal line refers to the Fermi level). Panels (c) and (d) are the same 