Anisotropy parameters

Here e is the depth of the well and d is the distance to zero crossing point of the isotropic potential whereas at and bt are anisotropy parameters. Substituting this potential into Eq. (5.50) we get for each anisotropic term [202]... 

It was shown in the preceding section that PECD can be anticipated to have an enhanced sensitivity (compared to the cross-section or p anisotropy parameter) to any small variations in the photoelectron scattering phase shifts. This is because the chiral parameter is structured from electric dipole operator interference terms between adjacent -waves, each of which depends on the sine of the associated channels relative phase shifts. In contrast, the cross-section has no phase dependence, and the p parameter has only a partial dependence on the cosine of the relative phase. The distinction between the sine... 

Figure 10. The CMS-Xa predictions for cross-section, the anisotropy parameter —P/2), and the chiral parameter in the carbonyl C li photoionization of (R)-carvone (I) and its indicated derivatives.

From the translational energy distributions obtained above, the quantum state distributions and the quantum state-specific anisotropy parameters can be determined. In a molecular photodissociation process, the photodissociation product detected at an angle in the center-of-mass... 

Fig. 13. The anisotropy parameters for the OH(X, = 0,1V) products. The two oscillation sites correspond exactly to the population oscillations exhibited in Fig. 11.

Fig. 14 are the simulated distributions including the different parent rotational levels. An interesting observation from these distributions is that the shape of the multiplet peak corresponding to each 011 (/I) rotational level for the perpendicular polarization is not necessarily the same as that for the parallel polarization see for example the peak labelled v = 0, N = 22. From the simulations, relative populations are determined for the OH (A) product in the low translational energy region from H2O in different rotational levels for both polarizations. The anisotropy parameters for the OH product from different parent rotational levels are determined. Experimental results indicate that the ft parameters for the 011 (/I) product from the three parent H2O levels Ooo, loi, I11, are quite different from each other. Most notably, for the 011 (/I, v 0, N = 22) product the ft parameter from the foi H2O level is positive while the ft parameters from the Ooo and In levels are negative, indicating that the parent molecule rotation has a remarkable effect on the product anisotropy distributions of the OH(A) product. The state-to-state cross-sections have also been determined, which also are different for dissociation from different rotational levels of H2O. 

Table 2. Singlet channel anisotropy parameter, / , results and comparison with results from other research groups.

The broad behavior of the anisotropy parameter versus speed curves is similar for all photolysis wavelengths. Unfortunately the 266 nm photolysis data at high 0(3P2) speeds was of insufficient quality to fit anisotropy parameters satisfactorily, so we cannot state with confidence whether the speed dependence of (3 changes at higher photolysis wavelengths. The overriding feature in Fig. 15 is the steady increase in [3 as the 0(3P2) fragments travel faster. Some structure is also apparent in the curves, with a plateau between approximately 1200 and 3700 m/s. 

The angular distributions of the 0(3P2) fragments show the degree of correlation between the product recoil velocity (v) with the electric vector of the dissociating light and are typically characterized by the lab frame anisotropy parameter (/ ) given in the equation,52,53... 

The anisotropy parameter is also sensitive to both the lifetime and geometry of the dissociating molecule. For an instantaneous dissociation, and... 

If the photolysis process is not immediate, but instead has some finite lifetime r, the parent molecule may have time to rotate during dissociation and so wash out the angular distribution. In this case a reduced effective anisotropy parameter (/3eff) is used to characterize the observed angular distribution. The relationship between [3eg and parent lifetime can be expressed as52,54... 

For dissociation at 226 and 230 nm, the determined j3 values for the fast and slow oxygen atoms are 1.3/1.5 and 0.7/0.8, respectively. The former value corresponds to a bond angle of 120°, close to the ozone ground state equilibrium bond angle of 117°. The reduced anisotropy parameter of 0.8 implies a more strongly bent geometry with a bond angle of 100°. 

The bimodal velocity distribution of the 0(3Pj) fragments produced via the triplet channel in the UV photodissociation of ozone has also been observed by Syage41,43>46 and Stranges et al.AA at photolysis wavelengths of 226 and 193 nm, respectively. Both authors measured anisotropy parameters for the fast and slow product pathways separately. 

Our determined anisotropy parameters for 226 nm photolysis agree favorably with the reported values of Syage, where a (3 value of 1.2 was measured for the fast 0(3P2) products. Syage observed a less anisotropic distribution for the slow 0(3P2) atoms, with a reported (3 value of 0.4. The f3 value of 1.2 for the high velocity component was rationalized by a prompt dissociation from the equilibrium ground state of ozone following an B I >2 <— X A i transition. 

Fig. 17. H-atom product channel translational energy distributions of the ethyl photodissociation, with the 245-nm photolysis radiation polarization (a) parallel to the TOF axis (b) at magic angle and (c) perpendicular to the TOF axis, and (d) anisotropy parameter /3(Et). In (b), the de-convoluted fast component, P[(i T), and slow-component, Pii(E ), are plotted in dashed and dotted lines, respectively. (From Amaral et al,39)...

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