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and Zoller 1981 ). This work required the use of a special procedure developed
to describe the continuum coupling because the widespread relaxation parameter
matrix method had proved to be inapplicable. Both RMPI and RMPD characteristics
revealed nonmonotonic variation in molecular dynamics with laser intensity (Joli-
card and Atabek 1992 ). This behavior is most clearly manifested in above-threshold
dissociation (ATD), which is significant at laser intensities I 10 13 W=cm 2
(Jolicard and Atabek 1992 ; Giusti-Suzor et al. 1990 ;Zavriyevetal. 1990 ). The
process competing with ATD is the ordinary single-photon absorption, and their
relative rates depend on the molecule's initial vibrational state and the laser intensity
and frequency. An increase in intensity to I 10 14 W=cm 2 has a considerable
bond-softening effect because the molecular potential is distorted by the laser
field (Zavriyev et al. 1990 ; Yao and Chu 1992 ). Details of the intensity-dependent
dynamics underlying these phenomena were examined by Yang et al. ( 1991 ). Laser
effects on molecular ions were investigated by Zavriyev et al. ( 1993 ) and Aubanel
et al. ( 1993 ). It should also be noted that a bichromatic driving field (the fundamental
harmonic and a phase-shifted higher one of the same laser) provides a means for the
coherent control of dissociation (Charron et al. 1994 ; Abrashkevich et al. 1998 ),
in particular for the isotope separation (Atabek et al. 1994 ; Charron et al. 1995 ).
These experimental observations stimulated theoretical studies intended to explain
and predict the laser-driven phenomena. Let us discuss these matters in some detail.
Two essentially different approaches were developed to solve problems of this kind
(e.g., see Giusti-Suzor et al. 1995 ;Guo 1998 ).
In one of these, the stationary equations of the Floquet theory are used (Shirley
1965 ), which is valid to describe processes driven by dye lasers with typical pulse
durations of 10 10 to 10 9 s, when the field is switched on at t D 0 and applied
for a sufficiently long time. The approach is true if the laser pulse is sufficiently
long and the process dynamics does not vary from cycle to cycle ( l r ,where
r is a reaction time). The total wave function is represented as a superposition of
dressed states, and the system of coupled equations is solved numerically (Chu
1991 ;Heetal. 1990 ; Bandrauk et al. 1993 ). For short laser pulses . l <10 12 s/,
the Schr odinger equation describing the time evolution of the emerging wave packet
is generally computed by using a Gaussian pulse shape. Finding of such solutions
is a formidable task. However, a number of assumptions can be made that greatly
simplify theoretical analysis, such as the one-dimensional approximation where
the internuclear vector is collinear to the laser polarization vector. The resulting
solution is only slightly different from those of the three-dimensional problem
(Charron et al. 1994 ).
The Role of Rotational Degrees of Freedom
One of the issues most widely discussed in the literature is the role of molecular
rotation (Ivanov et al. 1996 , 1997b ; Charron et al. 1994 ; Giusti-Suzor et al. 1995 ;
McCann and Bandrauk 1992 ; Banerjee et al. 1994 ; Sukharev and Krainov 1998 ),
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