Relaxation cross-section

Figure B2.2.3. Vibrational relaxation cross sections (quantal and semiclassical) as a fiinction of collision energy E.

Fig. 1.25. Temperature-dependence of rotational relaxation cross-section from [81], For the lowest temperature point the experimental uncertainty is indicated, the latter being the biggest one over the whole set of measurements.

Storozhev A. V., Strekalov M. L. Relaxation cross sections for transfer of rotational angular momentum in a semiclassical approximation, Chem. Phys. 153, 99-113 (1991). 

Bonamy L., Bonamy J., Robert D., Temkin S. I. Consequences of angular momenta coupling on generalized spectroscopic relaxation cross-sections collisional narrowing in isotropic and anisotropic Raman CO2 branches, Proc. 13th ICORS. (Wiley Sons, New York) (1992). 

Level crossing has been used rather widely in the case of atoms and ions in order to determine lifetime, Lande factors, fine and hyperfine structure constants and relaxation cross-sections of coherence (cri,a2). For deeper acquaintance with these questions we recommend monographs and reviews [6, 96, 228, 296, 300, 301, 314] and the literature cited therein. 

The determination of the concentration dependence of the width of the Hanle signal is widely used for measuring the relaxation cross-section of alignment <72, applying (2.42), where K = 2. As an example we may quote data from [312] given in Fig. 4.8, where a very large value of 02 = 1000 A2 was obtained for collisions K2(B1IIU) + K. 

How efficient is the described representation of the ArCC>2 potential To answer this question the above PES along with a few empirical potentials have been used to derive a number of properties, such as the ground vibrational state and dissociation energy of the complex, ground state rotational constants, the mean square torque, the interaction second virial coefficients, diffusion coefficients, mixture viscosities, thermal conductivities, the NMR relaxation cross sections, and many others [47]. Overall, the ab initio surface provided very good simulations of the empirical estimates of all studied properties. The only parameters that were not accurately reproduced were the interaction second virial coefficients. It is important that its performance proved comparable to the best empirical surface 3A of Bohac, Marshall and Miller [48], This fact must be greeted with satisfaction since no empirical adjustments were performed for the ab initio surface. 

For low temperature collisions with He, the fit given by the multiquantum jump model was clearly superior to that obtained using the single quantum jump model. Even so, the Av = —I process accounted for more than 70% of the total removal rate constant (a = 1.1). For transfer out of V = 23, the total removal rate constant was around 1.6 x 10" cm s at 5 K. This was roughly an order of magnitude smaller than the He vibrational relaxation rate constant at room temperature (1.7 x 10 cm s ). Part of this difference is from the change in the collision frequency. To compensate for this factor, it is helpful to calculate effective vibrational relaxation cross sections from the relationship = kv-v / v)i where v) is the average... 

E.I.Dashevskaya and E.E.Nikitin, Quasiclassical integral polarisation tranfer and relaxation cross sections in atomic collisions, Optika i Spektr. 62, 742 (1987)... 

State-specific rovibrational relaxation cross section (n [Pg.415]

Relaxed Cross Sections of Nuclear Configuration Spaces... 

By contrast, the line (2), y = x of the above example is a fully relaxed cross section of the energy function (1), since there the gradient is the constant vector (1,1), parallel with line (2) at all points. 

We may conclude that it is a somewhat misleading practice in computational conformational analysis and reaction surface studies to use the term "relaxed cross section" for the cross sections obtained with the usual method. The significance of this distinction has been pointed out in recent studies [2,3] where truly relaxed cross sections have special importance. Here, also, we shall need truly relaxed cross sections, since they have special properties which can be exploited in symmetry and shape analysis. 

As for the other partitionings mentioned above, these neighbor relations and graphs can be restricted to various subsets S, such as relaxed cross sections, and in particular, to individual catchment regions C(X,i) of the nuclear configuration space M. This approach leads to the local shape domain graphs g(S,x) and g(C(X,i),x), respectively. 

One may analyse the detailed variations of contributions of various nuclear configurations to each shape type Xj as a function of some continuous parameters, for example, as function of the contour density value a and reference curvature parameter b of isodensity contours G(a). This is equivalent to the analysis of the parameter dependence (for example, (a,b)-dependence) of the Ty subsets within the configuration space M, and in particular, in relaxed cross sections or within each catchment region C(X,i) [44]. These changes can be monitored within the dynamic shape space D, obtained as the product space of the nuclear configuration space M and the space of the actual continuous parameters. This approach has been described in some detail in ref. [44], and various applications can be found in refs. [45-47]. 

The DCS is a rich source of information about atomic and molecular interactions as it allows one to unfold the partial wave averaging and analyze each /-contribution separately [43]. In addition, spin relaxation cross-sections are extremely sensitive to the atom-molecule interaction potential [19]. Therefore, we expect the spin relaxation DCS to be a sensitive probe of the anisofropic molecular interactions. As shown in Section 4.2, electric fields enhance the / / 1 transitions, and thus the sensitivity of the cross-sections to the anisotropic part of the interaction potential. Figure 4.20 illustrates that spin relaxation DCSs assume a specific 0 dependence near a shape resonance, which can be used for detection and assignment of shape resonances in cold collisions. 

FIGURE 13.5 Trapped molecule lifetime vs. buffer-gas density (note semilog scale) for two hypothetical molecular species. For the dashed curve, the helium-induced Zeeman relaxation cross-section has been increased by a factor of 10. 

Rotational relaxation of HF by collision with rare gas atoms is of particular interest as a recent laser double-resonance measurement of rate coefficients for the relaxation of HF(j=13) has been made by Taatjes and Leone at room temperature[63]. Since a potential surface suitable for calculations on van der Waals dynamics in Ne-HF has recently become available[59], it is of interest to calculate the rotational relaxation cross sections and rates for Ne+HF(j=13->j ). We have done this using both the CC and CSA methods. The calculations were performed on the Convex Cl computer and it was necessary to include basis functions with j having a maximum value of 15 and minimum value of 9 in the CC computations (amounting to a 84 basis function calculation). 

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