Collisions anisotropic

Here the proportionality factor fp ( J d J") 2/(2J +l) coincides with the dynamic part of the absorption probability introduced in Chapter 2. The sum in (5.10) presents the angular part of the absorption probability, whilst the factor (rmm + 0 %M ) 1 describes the effect upon /mm both on the part of perturbation by the external field, causing splitting of the magnetic sublevels j ujmm i and by spontaneous decay and collisions (anisotropic in the general case), together described by a set of relaxation rates Tmm Applying similar manipulations as for (5.7) to Eq. (5.6), we obtain an equation for fluorescence intensity ... 

In the purely non-adiabatic limit the phase (5.52) coincides with that calculated in [203] and for very long flights (rt b,v" v) or high energies (.E e) it reduces to what can be obtained from the approximation of rectilinear trajectories. However, there is no need for these simplifications. The SCS method enables us to account for the adiabaticity of collisions and consider the curvature of the particle trajectories. The only demerit is that this curvature is not subjected to anisotropic interaction and is not affected by transitions in the rotational spectrum of the molecule. 

The rotational phase shift 5, which cannot exceed a mean angle of a molecular rotation during collisional time (anc), is certainly small in the case of non-adiabatic collisions. This condition is exactly that needed for anisotropic scattering (or IR absorption) spectrum narrowing, just as vibrational dephasing must be weak for an isotropic spectrum to narrow. 

The lower boundary corresponds to strong collisions, and the upper one to weak collisions. This conclusion can be confirmed by experiment. According to [259], nitrogen dissolved in SF6 has a symmetrical spectrum of isotropic scattering, indicating that collapse of the spectrum has already occurred. At the same densities, the Q-branch of the anisotropic spectrum is still well separated from the side branches, and in [259] the lower bound for its half-width is estimated as 5 cm-1. So,... 

Figure 4.9 illustrates time-gated imaging of rotational correlation time. Briefly, excitation by linearly polarized radiation will excite fluorophores with dipole components parallel to the excitation polarization axis and so the fluorescence emission will be anisotropically polarized immediately after excitation, with more emission polarized parallel than perpendicular to the polarization axis (r0). Subsequently, however, collisions with solvent molecules will tend to randomize the fluorophore orientations and the emission anistropy will decrease with time (r(t)). The characteristic timescale over which the fluorescence anisotropy decreases can be described (in the simplest case of a spherical molecule) by an exponential decay with a time constant, 6, which is the rotational correlation time and is approximately proportional to the local solvent viscosity and to the size of the fluorophore. Provided that... 

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

This question was addressed by use of classical trajectory techniques with an ion-quadrupole plus anisotropic polarizability potential to determine the collision rate constant (k ). Over one million trajectories with initial conditions covering a range of translational temperature, neutral rotor state, and isotopic composition were calculated. The results for the thermally average 300 K values for are listed in the last column of Table 3 and indicate that reaction (11) for H2/H2, D2/D2, and HD /HD proceeds at essentially the classical collision rate, whereas the reported experimental rates for H2/D2 and D2/H2 reactions seem to be in error as they are significantly larger than k. This conclusion raises two questions (1) If the symmetry restrictions outlined in Table 2 apply, how are they essentially completely overcome at 300 K (2) Do conditions exist where the restriction would give rise to observable kinetic effects ... 

Theory. The theory of collision-induced absorption profiles of systems with anisotropic interaction [43, 269] is based on Arthurs and Dalgamo s close coupled rigid rotor approximation [10]. Dipole and potential functions are approximated as rigid rotor functions, thus neglecting vibrational and centrifugal stretching effects. Only the H2-He and H2-H2 systems have been considered to date, because these have relatively few channels (i.e., rotational levels of H2 to be accounted for in the calculations). The... 

Venus atmosphere consists mainly of CO2 of high density. It is perhaps the least well understood atmosphere, because the existing laboratory studies of collision-induced absorption in carbon dioxide and the theoretical analyses attempted have revealed some unexpected complexity. Some of the problems mentioned have to do with the strong ternary components observed furthermore, the pair interaction is strongly anisotropic and the anisotropy has never been accounted for. More work is required for a better understanding (Tipping 1985). 

A. Borysow and M. Moraldi. Effects of anisotropic interaction on collision-induced absorption by pairs of linear molecules. Phys. Rev. Lett. 68 3686, 1992. 

M. Moraldi, A. Borysow, and L. Frommhold. Effects of the anisotropic interaction on collision induced rototranslational spectra of H2-He pairs. Phys. Rev., A 35 3679, 1987. 

Since longitudinal orientation /d can arise only from diagonal matrix elements /mm, which are not affected by external perturbation in the form of anisotropic collisions or in the form of an external field, at linearly polarized excitation we have /d = 0 irrespective of the type of perturbation. This means that the orientation which may emerge must be transversal, i.e. the corresponding components / of the polarization moment must appear. According to (5.40) we can write... 

The material presented so far was based on the creation of anisotropic distribution of molecular angular momenta under the direct effect of light absorption. We are now going to discuss briefly some ideas and examples of experimental realization of other methods leading to the production of polarized molecules, including those which are not directly connected with light effects, such as polarization caused by collisions and external electric or magnetic fields. 

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