  The structure of binary mixtures of bosonic and fermionic atoms in an
external trapping potential at zero temperature is studied on the basis of a
modified Gross-Pitaevskii equation for the bosonic component which
self-consistently includes the mean-field interaction generated by the
fermionic cloud. The density of the fermionic component is described within the
Thomas-Fermi approximation. The influence of the boson-boson and the
boson-fermion s-wave interaction on the density profiles and the stability of
the mixture is investigated systematically. Critical particle numbers for the
mean-field collapse caused either by attractive boson-boson or by attractive
boson-fermion interactions and for the onset of spatial component separation
are discussed. It is shown that the interplay between the boson-boson and the
boson-fermion interaction generates a rich and complex phase diagram. Finally,
the specific properties and prospects of the boson-fermion mixtures available
in present experiments are addressed.
