Rotational rainbow

Figure A3.9.5. Population of rotational states versus rotational energy for NO moleeules seattered from an Ag (111) surfaee at two different ineidenee energies and at = 520 K [25] (a) E = 0.85 eV, 0. = 15° and b) E = 0.09 eV, 9. = 15°. Results at = 0.85 eV show a pronoimeed rotational rainbow.

The apparently statistical distribution observed in the calculations for low J arose from several kinds of trajectories that combined to produce the observed distribution. The existence, position and magnitude of the rotational rainbow is sensitive to the orientational anisotropy of the attractive interaction potential (washed out by averaging), and does not result from anisotropies in the repulsive interaction region. 

Thermal distributions of NO(u 2, J, A Ej,) states were observed, wherein the population in any level was determined by the internal energy and the parameter Tr. and independent of spin-orbit state or lambda doublet species. This is in contrast to the rotational rainbows, the propensities for preferential population in the Il(A ) lambda doublet species and the Fj spin orbit state which were observed in direct inelastic scattering of NO/Ag(l 11). 

Second, the calculated (as well as the measured) distributions are remarkably smooth although often more than fifty or so rotational states are populated. If so many quantum states take part in a collision, one intuitively expects pronounced interference oscillations. The reason for the absence of interferences is the uniqueness between 70 and j one and only one trajectory contributes to the cross section for a specific final rotational state. If two trajectories that lead to the same j had comparable weights, the constructive and destructive interference, within a semiclassical picture, would lead to pronounced oscillations (Miller 1974, 1975 Korsch and Schinke 1980 Schinke and Bowman 1983). These so-called supernumerary rotational rainbows are well established in full collisions (Gottwald, Bergmann, and Schinke 1987). If the weighting function W (70) is sufficiently wide that both trajectories contribute to the dissociation cross section, similar oscillations may also exist in photodissociation (see, for example, Philippoz, Monot, and van den Bergh 1990 and Miller, Kable, Houston, and Burak 1992). 

Janda, K.C. and Bieler, C.R. (1990). Rotational rainbows, quantum interference, intramolecular vibrational relaxation and chemical reactions All in rare gas-halogen molecules, in Atomic and Molecular Clusters, ed. E.R. Bernstein (Elsevier, Amsterdam). 

Schinke, R. and Bowman, J.M. (1983). Rotational rainbows in atom-diatom scattering, in Molecular Collision Dynamics, ed. J.M. Bowman (Springer, Berlin). 

Figure 11 Final rotational state distributions for NO scattered from Ag(l 11) for different initial orientations measured at a final angle of 70° and at an incidence angle of 35°. The upper panel corresponds to NO initially oriented with the N-end towards the surface and shows approximately a Maxwell-Boltzmann distribution as given by the dotted line. The lower panel corresponds to NO initially oriented with the O-end towards the surface and shows a pronounced rotational rainbow. From Geuzebroek et al. [36],...

Fig. 2. Supernumerary rotational rainbow oscillations for the j = 0 2 transition in He + Na2 collisions. The dots are the...

Macdonald, R. and Liu, K., State-to-state integral cross sections for the inelastic scattering of CH(2f H) 4-He Rotational rainbow and orbital alignment, J. Chem. Phys., 91,821-838, 1989. 

Contents J.M.Bowman Introduction. - D.Secrest Inelastic Vibrational and Rotational Quantum Collisions. -G. C.Schatz Quasiclassical Trajectory Studies of State to State Collisional Energy Transfer in Polyatomic Molecules. - R. Schinke, J. M. Bowman Rotational Rainbows in Atom-Diatom Scattering. - M.Baer Quantum Mechanical Treatment of Electronic Transitions in Atom-Molecule Collisions. - Subject Index. 

At the high level of final state resolution provided by such experiments we can discern quantal interference effects. The more prominent feature for inelastic excitation is a rotational rainbow that arises by a mechanism similar to the intense scattering of the final velocity into certain directions (Section 2.2.5). Here too, the rainbow arises from different trajectories scattered into the same final state except that the state is specified not only by the direction of v but also by the rotational state of the molecule, NO in the case of Figure 10.9. This is a stereodynamic effect because the final state is determined not only by the impact parameter but also by the angle of approach, as shown for scattering by a hard ellipsoid in Figure 10.10. 

Among the many recent applications of sudden approximations, we mention those to rotational rainbows in T-R transfer,magnetic transitions in atom-diatom T-R transfer,T-(R,V) transfer in He-C02... 

J. M. Bowman, Rotational rainbows in inelastic atom-molecule differential cross sections, Chem. Phys. Lett. 62 309 (1979). 

Another approximation which has been used to study rotational rainbows is the quantum mechanical lOS approximation. (Eor a review and extensive references to the original lOS literature see reference 51.) Possibly the best example of this is the good agreement between lOS calculations and experiment for He-Na2 collisions. 

K. Bergmann, U. Hefter, A. Mattheus, and J. Witt, Resolution of angular rotational rainbows in Na2 Ne collisions, preprint (March, 1980). 

R. Schinke and P. McGuire, Rotational rainbow oscillations in He-Na2 collisions Comparison between coupled states and infinite order sudden approximations, J. Chem. Phys. 71 4201... 

R. Schinke, Rotational rainbow maxima A time dependent study, Chem. Phys. 47 287 (1980). 

R. Schinke, W. Muller, W. Meyer, and P. McGuire, Theoretical investigation of rotational rainbow structures in X-Na2 collisions using Cl potential surfaces. I. Rigid-rotor X=He scattering and comparison with state-to-state experiments, J. Chem. Phys., submitted for publication. 

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