Differential cross sections product state distributions

D. Partial Cross Sections, Product State Distributions, and Differential Cross Sections III. Reactive Scattering Theory... 

PARTIAL CROSS SECTIONS. PRODUCT STATE DISTRIBUTIONS. AND DIFFERENTIAL CROSS SECTIONS... 

The most important observable is the angular distribution of the scattered products with respect to the initial approach direction of the reagents, which is called the state-to-state differential cross-section (DCS). The DCS can be written [57-61]... 

In the context of the present chapter, only the differential cross-section (DCS) results will be reviewed.27,31 The DCS obtained by experiment and theory27 are shown in Figs. 17-19. In Fig. 17 we show the experimental total angular distributions, da/dfl, around the 0.5 kcal/mol feature obtained by summing over all (vj ) states of the HF products. (The resolution was sufficiently high to resolve most of the product rovibrational states for j > 4... 

The bulk of the experimental material involves an additional integration over all internal energies v,b. rot of the product-state distribution. As a consequence, no detailed theoretical prediction on differential cross sections d2a/dUCMdEvib rot have emerged so far. 

Finally, Fig. 4.1.15 shows the differential cross-section dan/dd, which gives the angular distribution of product molecules independently of their quantum state. The differential cross-section shows a peak for backward scattering (0 = 180°) with the... 

Chemical dynamics experiments in which OH product quantum state distributions and an absolute reaction cross section for reaction (1) could be measured were reported in 1984. Subsequent experiments revealed additional details about the reaction dynamics, including nascent OH( H) spin-orbit and A-doublet rotational fine structure state distributions, Oi P) product fine structure state distributions, and OH angular momentum polarization distributions,as well as differential cross sections. The experimental results indicate that depending on the reagent collision energy... 

Additional theoretical refinement is needed before we can quantitatively compare BCRLM differential cross sections with 3D. The shape of the BCRLM differential cross section contains information about the impact parameter dependence of the reaction probability, and whenever the 3D angular distribution retains only this level of dynamical detail, we would expect the BCRLM differential cross section to compare nicely. Consequently, it is likely that BCRLM will fare best when compared to 3D differential cross sections from the ground state of reactants to all product rotational states, since this type of cross section retains the least amount of rotational Information. 

The dlstorted wave Born-approximation (DWBA) is a quantum technique for calculating differential cross sections, integral cross sections and product state distributions for three dimensional (3D) chemical reactions of the type... 

The general conclusion from these comparisons for Hp is that the different DW theories give qualitatively similar results for relative quantities such as state-to-state differential cross sections and rotational product distributions. Howover. the absolute values of cross sections are different in the various DW theories, the order being SSDW < VADW < RADW < CADW s exact. This order Illustrates that as systematically better approximations (based on physical understanding) are made to the exact wavefunction the T matrix element (16). the magnitudes of the... 

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