Impact theory of orientational relaxation

Debye s theory, considered in Chapter 2, applies only to dense media, whereas spectroscopic investigations of orientational relaxation are possible for both gas and liquid. These data provide a clear presentation of the transformation of spectra during condensation of the medium (see Fig. 0.1 and Fig. 0.2). In order to describe this phenomenon, at least qualitatively, one should employ impact theory. The first reason for this is that it is able to describe correctly the shape of static spectra, corresponding to free rotation, and their impact broadening at low pressures. The second (and main) reason is that impact theory can reproduce spectral collapse and subsequent pressure narrowing while proceeding to the Debye limit. 

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Comparison of formulae (2.51) and (2.64) allows one to understand the limits and advantages of the impact approximation in the theory of orientational relaxation. The results agree solely in second order with respect to time. Everything else is different. In the impact theory the expansion involves odd powers of time, though, strictly speaking, the latter should not appear. Furthermore the coefficient /4/Tj defined in (2.61) differs from the fourth spectral moment I4 both in value and in sign. Moreover, in the impact approximation all spectral moments higher than the second one are infinite. This is due to the non-analytical nature of Kj and Kf in the impact approximation. In reality, of course, all of them exist and the lowest two are usually utilized to find from Eq. (2.66) either the dispersion of the torque (M2) or related Rq defined in Eq. (1.82) ... 

Chapter 3 is devoted to pressure transformation of the unresolved isotropic Raman scattering spectrum which consists of a single Q-branch much narrower than other branches (shaded in Fig. 0.2(a)). Therefore rotational collapse of the Q-branch is accomplished much earlier than that of the IR spectrum as a whole (e.g. in the gas phase). Attention is concentrated on the isotropic Q-branch of N2, which is significantly narrowed before the broadening produced by weak vibrational dephasing becomes dominant. It is remarkable that isotropic Q-branch collapse is indifferent to orientational relaxation. It is affected solely by rotational energy relaxation. This is an exceptional case of pure frequency modulation similar to the Dicke effect in atomic spectroscopy [13]. The only difference is that the frequency in the Q-branch is quadratic in J whereas in the Doppler contour it is linear in translational velocity v. Consequently the rotational frequency modulation is not Gaussian but is still Markovian and therefore subject to the impact theory. The Keilson-... 

The orientational relaxation, considered in Chapters 6 and 7, is a more complex problem. The impact theory is the only model capable of tracing the transition from quasi-free rotation in the rare gas to... 

Now we refer to the analysis of a functional relationship between the times of orientational and rotational (angular momentum) relaxation that are rg/ and tj, respectively. To lowest order in Jf/, this relationship is given by the Hubbard relation (2.28). It is universal in the sense that it does not depend on the mechanisms of rotational relaxation. However, this relation does not hold when rg/ is calculated to higher order in Jf/. Corrections to the Hubbard relation are expressed in terms of higher correlation moments of co,(t) whose dependence on tj is specific for different mechanisms. Let us demonstrate this, taking the impact theory as an example. In principle it distinguishes correlated behaviour of the... 

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