  A variational theory is presented of A$^{1-}$ and A$^{2-}$ 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 magneto-transport 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.
