Abstract
There are many experimental and theoretical investigations devoted to the multiphoton ionization (MPI) and above threshold ionization (ATI) of atoms in a laser field. Most of them are carried out for the ionization of atoms in ground states. But atoms in highly excited states with large orbital moments behave different from atoms in ground states when exposed to a laser field. Investigations of stability of atoms in Rydberg states in strong laser fields theoretically are carried out using methods of classical mechanics by Vos and Gavrila (1992) and Shepelansky. For not very intensive laser fields perturbation theory may be used. But up to now using perturbation theory are investigated only ionization from ground states and excited states with main quantum number n not higher than ten. The simplest is to investigate hydrogen atom as for it analytical expressions for transition matrix elements can be written. Investigating behavior of Rydberg states one have to get asymptotic expressions for them in the case of large main quantum number n and orbital momentum otherwise they diverge.
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