A variational theory is presented of A1− and A2− centers, i.e., of a negative acceptor ion localizing one and two conduction electrons, respectively, in a GaAs/GaAlAs quantum well in the presence of a magnetic field parallel to the growth direction. A combined effect of the well and magnetic field confines conduction electrons to the proximity of the ion, resulting in discrete repulsive energies above the corresponding Landau levels. The theory is motivated by our experimental magnetotransport results which indicate that, in a heterostructure doped in the GaAs well with Be acceptors, one observes a boil-off effect in which the conduction electrons in the crossed-field configuration are pushed by the Hall electric field from the delocalized Landau states to the localized acceptor states and cease to conduct. A detailed analysis of the transport data shows that, at high magnetic fields, there are almost no conducting electrons left in the sample. It is concluded that one negative acceptor ion localizes up to four conduction electrons.