  We study the interaction-induced localization -- the so-called self-trapping
-- of a neutral impurity atom immersed in a homogeneous Bose-Einstein
condensate (BEC). Based on a Hartree description of the BEC we show that --
unlike repulsive impurities -- attractive impurities have a singular ground
state in 3d and shrink to a point-like state in 2d as the coupling approaches a
critical value. Moreover, we find that the density of the BEC increases
markedly in the vicinity of attractive impurities in 1d and 2d, which strongly
enhances inelastic collisions between atoms in the BEC. These collisions result
in a loss of BEC atoms and possibly of the localized impurity itself.
