  Ground-state solutions in a dilute gas interacting via contact and magnetic
dipole-dipole forces are investigated. To the best of our knowledge, it is the
first example of studies of the Bose-Einstein condensation in a system with
realistic long-range interactions. We find that for the magnetic moment of e.g.
chromium and a typical value of the scattering length all solutions are stable
and only differ in size from condensates without long-range interactions. By
lowering the value of the scattering length we find a region of unstable
solutions. In the neighborhood of this region the ground state wavefunctions
show internal structures not seen before in condensates. Finally, we find an
analytic estimate for the characteristic length appearing in these solutions.
