Collision resonant scattering

Mies F H 1969 Resonant scattering theory of association reactions and unimolecular decomposition. Comparison of the collision theory and the absolute rate theory J. Cham. Phys. 51 798-807... 

In ordinary unimolecular reaction rate theory, the usual assumptions of strong collisions and random distribution of the internal energy simply serve to wash out precisely those features of the molecular dynamics that become of primary importance in the cases of photochemical, chemical, and electron impact excitation. Whereas evaluation of all the consequences is incomplete at present, it is already clear that the representation of an excited molecule in terms of the properties of resonant scattering states holds promise for the elucidation of those aspects of the internal dynamics that are important in photochemistry. 

In addition to laser fluorescence excitation, several other laser spectroscopic methods have been found to be useful for the state-selective and sensitive detection of products of reactive collisions resonance-enhanced multiphoton ionization [58], coherent anti-Stokes Raman scattering [M], bolometric detection with laser excitation [30], and direct infrared absorption [7]. Several additional laser techniques have been developed for use in spectroscopic studies or for diagnostics in reacting systems. Of these, four-wave mixing [ ] is applicable to studies of reaction dynamics although it does have a somewhat lower sensitivity than the techniques mentioned above. 

Fig. 8.10 Laser-induced Feshbach resonance scattering length a (in terms of the Bohr radius ao) (solid line) and inelastic-collision rate coefficient Ainei (dashed line) as a function of the detiming of the laser from the photoassociation resonance for typical parameters of Inset schematic diagram of the optical coupling of the scattering unbound state A with the excited bound state B. (Reprinted from Theis et al. 2004 with courtesy and permission of the American Physical Society.)...

At the time the experiments were perfomied (1984), this discrepancy between theory and experiment was attributed to quantum mechanical resonances drat led to enhanced reaction probability in the FlF(u = 3) chaimel for high impact parameter collisions. Flowever, since 1984, several new potential energy surfaces using a combination of ab initio calculations and empirical corrections were developed in which the bend potential near the barrier was found to be very flat or even non-collinear [49, M], in contrast to the Muckennan V surface. In 1988, Sato [ ] showed that classical trajectory calculations on a surface with a bent transition-state geometry produced angular distributions in which the FIF(u = 3) product was peaked at 0 = 0°, while the FIF(u = 2) product was predominantly scattered into the backward hemisphere (0 > 90°), thereby qualitatively reproducing the most important features in figure A3.7.5. 

Cross-sections for reactive scattering may exhibit a structure due to resonance or to other dynamical effects such as interference or threshold phenomenon. It is useful to have techniques that can identify resonance behavior in a system and distinguish it from other sorts of dynamics. Since resonance is associated with dynamical trapping, the concept of the collision time delay proves quite useful in this regard. Of course since collision time delay for chemical reactions is typically in the sub-picosecond domain, this approach is, at present, only useful in analyzing theoretical scattering results. Nevertheless, time delay is a valuable tool for the theoretical identification of reactive resonances. 

Fig. 3. The normalized excitation functions in A2 versus collision energy for the two isotopic channels for the F+HD reaction. The solid line is the result of quantum scattering theory using the SW-PES. The QCT simulations from Ref. 71 are plotted for comparison. The experiment, shown with points, is normalized to theory by a single scaling factor for both channels. Also shown in (a) is the theoretical decomposition of the excitation function into direct and resonant contributions using the J-shifting procedure.

In summary, the reactive resonance for the F + HD —> HF + D reaction is found to leave clear signatures on a variety of collision observables. The resonance state itself is readily extracted from the quantum dynamics on the SW-PES, and the scattering observables are found to correlate well with the predictions of theory. 

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