Ionization of a quantum system with a short-range potential by a linearly p
olarized field is numerically studied within a wide range of laser intensit
ies and frequencies. The dynamics of such a system is interpreted in terms
of both Kramers-Henneberger eigenstates and field-free atomic states. The e
xact solution is analyzed to determine which potential (atomic or Kramers-H
enneberger potential) provides the most adequate physical description of th
e ionization of the system. The validity of the Kramers-Henneberger approac
h is examined, in particular, for low laser frequencies. In addition to the
condition obtained by Gavrila and Kaminski, we found another, stronger lim
itation on the validity range of the Kramers-Henneberger approximation. Low
-frequency stabilization is shown to occur only if the Kramers-Henneberger
approach is physically correct and is applied within its validity range.