Opacity function for

Figure 4 Opacity function for the H + H20(004) —> OH + H2 reaction at various initial relative kinetic energies...

Fig. 17. The angle-dependent integrated opacity function dan(00 —> v = 0,1, f = 0 6, Eq, Jmax) versus Jmax computed for the experimental energy Eq = 1.200eV. This quantity is computed by restricting the partial wave sum in the DCS to the terms J < Jmax- The result is shown for forward and backward scattering to illustrate the J-contributions to scattering at different 0.

Present theoretical efforts that are directed toward a more complete and realistic analysis of the transport equations governing atmospheric relaxation and the propagation of artificial disturbances require detailed information of thermal opacities and long-wave infrared (LWIR) absorption in regions of temperature and pressure where molecular effects are important.2 3 Although various experimental techniques have been employed for both atomic and molecular systems, theoretical studies have been largely confined to an analysis of the properties (bound-bound, bound-free, and free-free) of atomic systems.4,5 This is mostly a consequence of the unavailability of reliable wave functions for diatomic molecular systems, and particularly for excited states or states of open-shell structures. More recently,6 9 reliable theoretical procedures have been prescribed for such systems that have resulted in the development of practical computational programs. 

Figure 4 Quasi-classical opacity function P(p), defined as the fraction of reactive trajectories for a given impact parameter, p (solid line). Also plotted is Krei, the component of the relative incident-target H atom kinetic energy parallel to the surface, following a non-reactive collision (dotted line). The results correspond to H-on-D for the flat-surface potential described in the text.

A few words on the form of P, (p) are in order. Our opacity is very different from that often encountered in textbooks of gas phase reactions, where P, is assumed to be constant up to some value of p, and zero beyond that. Similar holes (regions of low reactivity at low p) in the opacity function have been computed for the ER reactions of H(g) with Cl adsorbed onto Au( 1 1 1) [91,92] and with H physisorbed onto graphite [85]. For H atoms on a corrugated Cu(l 1 1) surface we find smaller holes than in Fig. 4, but the reactivity still becomes small near zero impact [38]. Note that the reaction cross section, defined as... 

We have also computed reaction probahilities for H2(i = O.j = 0) and. / > 0. The opacity functions P J) (total reaction probability as a function of total angular momentum J at a fixed oiiorg> ) arc plotted in figure 6 for four colfision oiiorgios (25, 56, 84 tmd 100 me ). 

At any total scattering energy E, elements of the multichannel S matrix In the RLM are labelled by the total angular momentum Index I, and by the Initial and final vibrational quantum numbers v and v. Equations for physical observables in the BCRLM have been given previously (24-26), and we only summarize the final results here, In order to establish a common notation. The opacity function gives the Impact parameter dependence of the reaction probabilities. 

HF(v =2)+H at E 1.807 eV. The solid curve Is the direct result of the extraction procedure discussed In the text, and the dashed curve Is a smoothed version. The dotted curve reproduces the opacity function of Figure 1 for comparison. 

Figure 9. Background angular distributions for the reaction F+H2(v=0) + HF(v = 2)+H at E - 1.807 eV. The solid curve Is based on the opacity function shown In Figure 7 as a solid curve, and the smoother, dashed curve shows the angular distribution which results from the smoothed opacity function of Figure 7.

The F-HH2 reaction on this newer potential surface demonstrates one way In which the BCRLM will produce an angular distribution at the reaction threshold which Is not smooth and backward-peaked. In this case, the absence of a significant reaction probability for low partial waves, and the appearance of a resonance feature at larger partial waves, combine to produce an opacity function which peaks at large partial waves, and hence an angular distribution which has a predominant forward distribution of reaction products. Ve have seen results similar to these (41) In the angular distribution for the reactions F+D2(v 0) DF(v 3,4)+D on this same surface. 

Figure 12. Opacity functions at several energies for the reaction F+H2(v=0) + HF(v 2)+H on surface 3 of reference 41.

A generalized opacity function P, may simply be defined by rearranging the expression for oba in terms of the S matrix, to obtain... 

The influence of chemical reactions on elastic scattering has been extensively studied in the past. Nearly all treatments are based on the optical model (for a review see Ross and Green, 1970). Both the imaginary part of the potential (here assumed to be local) and the opacity function have been parameterized (Mariott and Micha, 1969 Harris and Wilson, 1971 and references cited therein). For a study of the total cross section see Diiren et al. (1972), A semiclassical study of a bimolecular exchange reaction where the three atoms are constrained to move on a straight line but the whole system is free to rotate in three dimensions, predicts a new kind of rainbow (Connor and Child, 1970),... 

---