  Studies of atomic systems in electric fields are challenging because of the
diverging perturbation series. However, physically meaningful Stark shifts and
ionization rates can be found by analytical continuation of the series using
appropriate branch cut functions. We apply this approach to low-dimensional
hydrogen atoms in order to study the effects of reduced dimensionality. We find
that modifications by the electric field are strongly suppressed in reduced
dimensions. This finding is explained from a Landau-type analysis of the
ionization process.
