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Note that the account of the strong field effect on the intermediate complex
differs substantially from the traditional time-dependent theory of the laser radiation
interaction with atoms and molecules (Delone and Krainov 1985 , 1994 , 2001 ),
because the formation time of the intermediate state cannot be well defined in the
quantum mechanical framework, and the coupling between closed channels and
continua must be taken into account in the analysis. These requirements motivated
the use of special methods for analyzing of the processes (1)-(3) in studies
performed in the 1990s. In particular, analysis of the elastic electron scattering by
the atomic hydrogen ions in the excimer laser field using numerical integration of
the strong coupling equations detected the fine resonance structure in the scattering
cross section (Dimou and Faisal 1987b ). Analogous features were also demonstrated
by Collins and Csanak ( 1991 ). Behavior of the Rydberg electrons in laser fields was
considered in the theory of radiative collisions of slow electrons with atoms (Giusti-
Suzor and Zoller 1987 ) and molecular ions (Ivanov et al. 1988 ) and in studies of
the photodissociation and photoionization of diatomic molecules (He et al. 1989 ;
Vartazaryan et al. 1989 ). Laser-assisted collisions involving bremsstrahlung from
electrons were also analyzed in (Berson 1981 ; Krainov and Roshchupkin 1983 ;
Lisitsa and Savel'ev 1987 ; Balashov et al. 1984 ; Klinskikh and Rapoport 1987 ).
2.3
Multiphoton Processes
The problem of laser field effect on the near-threshold photoabsorption spectra in
the processes (1) is closely related to that of the multiphoton ionization of atoms
(Rapoport et al. 1978 ). Compared to atoms, molecules are more complex quantum
systems where the key role is played by nonadiabatic coupling between the elec-
tronic and nuclear degrees of freedom (Golubkov and Ivanov 2001 ). In particular,
the theory of near-threshold photoionization must not only describe vibrational
and rotational dynamics but also rigorously take into account a predissociation.
Characteristics of the molecular structure play an important role in bound-bound
and bound-free radiative transitions (Lisitsa and Savel'ev 1987 ), which makes the
well-developed theory of electron-atom and electron-ion bremsstrahlung (Bunkin
and Fedorov 1966 ;Berson 1981 ; Krainov and Roshchupkin 1983 ; Lisitsa and
Savel'ev 1987 ) inapplicable to Rydberg molecules.
Laser-assisted interaction of an electron with a target involves emission by
stimulated bremsstrahlung and the absorption of field photons. The problem of the
laser-assisted bremsstrahlung emission and absorption was originally analyzed in
the Born approximation (Bunkin and Fedorov 1966 ). The electron-field interaction
was taken into account accurately in this work, i.e., the electron wave functions
(4) were employed. The authors have found the transition probabilities as the
sum of the probabilities of absorption (emission) of a definite number of field
photons. To go beyond the Born approximation, a semiclassical impact-parameter
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