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Existence criteria for stabilization from the scaling behaviour of ionization probabilities
We provide a systematic derivation of the scaling behaviour of various
quantities and establish in particular 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 consistency check in explicit
analytical expressions, in perturbation theory, in the Kramers-Henneberger and
Floquet approximation, in upper and lower bound estimates and fully numerical
solutions of the time dependent Schroedinger equation. The scaling invariance
leads to a differential equation which has to be satisfied by the ionization
probability and which yields an alternative criterium for the existence of
atomic bound state stabilization.Comment: 12 pages of Latex, one figur
Stabilization not for certain and the usefulness of bounds
Stabilization is still a somewhat controversial issue concerning its very
existence and also the precise conditions for its occurrence. The key quantity
to settle these questions is the ionization probability, for which hitherto no
computational method exists which is entirely agreed upon. It is therefore very
useful to provide various consistency criteria which have to be satisfied by
this quantity, whose discussion is the main objective of this contribution. We
show how the scaling behaviour of the space leads to a symmetry in the
ionization probability, which can be exploited in the mentioned sense.
Furthermore, we discuss how upper and lower bounds may be used for the same
purpose. Rather than concentrating on particular analytical expressions we
obtained elsewhere for these bounds, we focus in our discussion on the general
principles of this method. We illustrate the precise working of this procedure,
its advantages, shortcomings and range of applicability. We show that besides
constraining possible values for the ionization probability these bounds, like
the scaling behaviour, also lead to definite statements concerning the physical
outcome. The pulse shape properties which have to be satitisfied for the
existence of asymptotical stabilization is the vanishing of the total classical
momentum transfer and the total classical displacement and not smoothly
switched on and off pulses. Alternatively we support our results by general
considerations in the Gordon-Volkov perturbation theory and explicit studies of
various pulse shapes and potentials including in particular the Coulomb- and
the delta potential.Comment: 12 pages Late
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