  We investigate the properties a mobile ion immersed in a Bose-Einstein
condensate (BEC) using different theoretical approaches. A coherent state
variational ansatz predicts that the ion spectral function exhibits several
branches in addition to polaronic quasiparticle states, and we employ a
diagrammatic analysis of the ion-atom scattering in the BEC to identify them as
arising from the binding of an increasing number of bosons to the ion. We
develop a simplified model describing the formation of these molecular ions
showing that their spectral weight scales with the number of bound atoms. The
number of atoms in the dressing cloud around the ion are calculated from
thermodynamic arguments, and we finally show that the dynamics ensuing the
injection of an ion into the BEC exhibits various regimes governed by coherent
quasiparticle propagation and decay.
