Geoscience Reference

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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