Analytical treatment of stabilization

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