  We present a summarizing account of a series of investigations whose central
topic is to address the question whether atomic stabilization exists in an
analytical way. We provide new aspects on several issues of the matter in the
theoretical context when the dynamics is described by the Stark Hamiltonian.
The main outcome of these studies is that the governing parameters for this
phenomenon are the total classical momentum transfer and the total classical
displacement. Whenever these two quantities vanish, asymptotically weak
stabilization does exist. For all other situations we did not find any evidence
for stabilization. We found no evidence that strong stabilization might occur.
Our results agree qualitatively with the existing experimental findings.
