Existence criteria for stabilization from the scaling behaviour of ionization probabilities

We provide a systematic derivation of the scaling behaviour of various quan tities and, in particular, establish the scale invariance of the ionization probability. We discuss the gauge invariance of the scaling properties and the manner in which they can be exploited as a consistency check in explic it analytical expressions, in perturbation theory, in the Kramers-Henneberg er and Floquet approximations, in upper and lower bound estimates and fully numerical solutions of the time dependent Schrodinger equation. The scalin g invariance leads to a differential equation which has to be satisfied by the ionization probability and which yields an alternative criterion for th e existence of atomic bound state stabilization.