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    "description": "A new consistent method for studying the interaction of atom with a realistic laser field, based on the quantum electrodynamics (QED) and S-matrix adiabatic formalism Gell-Mann and Low, is presented. In relativistic case the Gell-Mann and Low formula expressed an energy shift \u03b4E through QED scattering matrix including the interaction with as the laser field as the photon vacuum field. It is natural to describe the laser field-atom interaction by means of the radiation emission and absorption lines. Their position and shape fully determine the spectroscopy of atom in a field. The radiation atomic lines can be described by moments of different orders \u03bcn. The main contribution into \u03bcn is given by the resonant range. The values \u03bcn can be expanded into perturbation theory (PT) series. As example, the method is used for numerical calculation of the three-photon resonant, four-photon ionization profile of atomic hydrogen (1s-2p transition; wavelength = 365 nm) and multi-photon resonance width and shift for transition 6S-6F in the atom of Cs (wavelength 1,059 nm) in a laser pulses with the Gaussian and soliton-like shapes. The results of calculation the above threshold ionization (ATI) characteristics for atom of magnesium field are presented too.", 
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