  We obtain the phase diagram of the double-exchange model at low electronic
densities in the presence of electron-electron interactions. The single
particle problem and its extension to low electronic densities, when a Wigner
crystal of magnetic polarons is generated due to unscreened Coulomb
interactions, is studied. It is argued that the Wigner crystal is the natural
alternative to phase separation when the Coulomb interaction is taken into
account. We discuss the thermal and quantum stability of the crystalline phase
towards a polaronic Fermi liquid and a homogeneous, metallic, ferromagnetic
phase. The relevance and application of our results to EuB_6 is also
considered.
