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the electronic structure of the molecule (Ivanov and Golubkov 1999 ). Accordingly,
a field is naturally referred to as strong if it is weak on an atomic scale but is strong
enough to mix the states of a Rydberg molecule XY ** that are stationary (or quasi-
stationary) in the absence of an external field. If the mixing strengths are large, then
perturbative treatment is inapplicable (Rosenberg 1982 ).
To date, a variety of methods have been developed for modeling laser-induced
nonlinear resonances embedded in the continua (Geller and Popov 1981 ), inter-
ference between autoionizing states in strong laser fields (Gontier and Nrahin
1980 ;Zakrewski 1984 ; Bachau et al. 1986 ; Movsesyan and Fedorov 1989 ),
adiabatic stabilization of excited states of atoms in strong laser fields (Fedorov
and Movsesyan 1988 ; Fedorov 1987 ; Horbatsch 1981 ;Suetal. 1990 ; Dubrovskii
et al. 1991 ; Gavrila 1992 ; Peatross et al. 1992 ; Vos and Gavrila 1992 ), multiphoton
ionization (Hoogenraad et al. 1994 ;Ivanovetal. 1994 , 1997a ; Delone and Krainov
1995 ; Moiseyev and Cederbaum 1999 ; Fedorov 1999 ; Kundliya and Mohan 2001 ;
Theodosiou et al. 1979 ;Reiss 1987 ; Fedorov and Ivanov 1990 ), and other phenom-
ena (Connerade et al. 1982 ; Jetzke et al. 1987 ; Bucksbaum et al. 1992 ; Zavriev and
Bucksbaum 1993 ;BrumerandShapiro 1993 ; Meyerhofer 1997 ; Akramine et al.
1999 ; Makhoute and Khalil 2008 ; Deb and Sinha 2009 ; Purohit and Mathur 2010 ;
Musa et al. 2010 ; Andryushin et al. 1982 , 1985 ; Fedorov and Roshchupkin 1984 ;
Akulin and Karlov 1987 ; Delone and Fedorov 1989 ;Ivanovetal. 1996 ; Khalil et al.
1997 ; Deb et al. 2009 ; Itatani et al. 2004 ).
The main differences between the radiative collisions and collisions occurring
in the absence of the field should be highlighted. First of all, the external field
influences the asymptotic states of colliding particles, so instead of the usual
solutions taken in the form of the plane waves, it is necessary to involve the state
describing the motion of particles in the presence of the field. With this purpose, the
“dressed” (Cohen-Tannoudji and Reynaud 1977 ) or the quasi-energy (Zel'dovich
1973 ) states are used. In both cases, the total wave function is expanded into an
infinite series, each term of which corresponds to a particular photon number in
the field; that is, account is taken of the virtual absorptions and emissions that
are kinematically forbidden because of the momentum conservation. Thus, the
problem is reduced to calculating the transition probabilities between the dressed
asymptotic states. Moreover, some processes can be only field induced. Actually,
at the expense of photon emission in the effective area of the interaction, total
energy of the quantum system can decrease to the level corresponding to its
bound state, which in this case will be unstable because of an exchange of energy
with the field. Such states are referred to as laser-induced resonances . The best
understanding of the physics of radiative collisions has been achieved in the low-
frequency approximation, which decouples the projectile-field and projectile-target
interactions and thus greatly simplifies the analysis of the system's behavior (Kelsey
and Rosenberg 1979 ; Rosenberg 1989 ).
The nonperturbative analysis of laser-assisted collisional processes was initiated
by Bunkin and Fedorov ( 1966 ), where the electron-atom bremsstrahlung stimulated
by the single-mode electromagnetic field was calculated. A similar treatment was
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