Momentum relaxation

This is no longer the case when (iii) motion along the reaction patir occurs on a time scale comparable to other relaxation times of the solute or the solvent, i.e. the system is partially non-relaxed. In this situation dynamic effects have to be taken into account explicitly, such as solvent-assisted intramolecular vibrational energy redistribution (IVR) in the solute, solvent-induced electronic surface hopping, dephasing, solute-solvent energy transfer, dynamic caging, rotational relaxation, or solvent dielectric and momentum relaxation. 

Though these are alternative models, they are both particular cases of the non-adiabatic impact theory of angular momentum relaxation in gases. Thus, we prefer to call them models of weak and strong collisions , as is usually done in analogous problems [13, 33],... 

Judging by these results the angular momentum relaxation in a dense medium has the form of damped oscillations of frequency jRo = (Rctc/to)i and decay decrement 1/(2tc). This conclusion is quantitatively verified by computer experiments [45, 54, 55]. Most of them were concerned with calculations of the autocorrelation function of the translational velocity v(t). However the relation between v(t) and the force F t) acting during collisions is the same as that between e> = J/I and M. Therefore, the results are qualitatively similar. In Fig. 1.8 we show the correlation functions of the velocity and force for the liquid state density. Oscillations are clearly seen, which point to a regular character of collisions and non-Markovian nature of velocity changes. 

The theory of Section 1.8 is sometimes qualified as non-Markovian since it accounts for non-exponential angular momentum relaxation, unlike impact theory which is Markovian in this sense. However, it is not a unique non-Markovian generalization of impact theory. Not less known is a differential version of the theory... 

In the impact approximation (tc = 0) this equation is identical to Eq. (1.21), angular momentum relaxation is exponential at any times and t = tj. In the non-Markovian approach there is always a difference between asymptotic decay time t and angular momentum correlation time tj defined in Eq. (1.74). In integral (memory function) theory Rotc is equal to 1/t j whereas in differential theory it is 1/t. We shall see that the difference between non-Markovian theories is not only in times but also in long-time relaxation kinetics, especially in dense media. 

Experimental data on nitrogen obtained from spin-lattice relaxation time (Ti) in [71] also show that tj is monotonically reduced with condensation. Furthermore, when a gas turns into a liquid or when a liquid changes to the solid state, no breaks occur (Fig. 1.17). The change in density within the temperature interval under analysis is also shown in Fig. 1.17 for comparison. It cannot be ruled out that condensation of the medium results in increase in rotational relaxation rate primarily due to decrease in free volume. In the rigid sphere model used in [72] for nitrogen, this phenomenon is taken into account by introducing the factor g(ri) into the angular momentum relaxation rate... 

Fig. 1.17. The temperature-dependence of angular momentum relaxation time (+) in nitrogen [71] and accompanying density change due to cooling (0).

Fig. 1.23. Density-dependence of angular momentum relaxation rate. Points correspond to experimental data presented in Fig. 1.17. The straight solid line is a binary estimation of this rate with the cross-section Oj = 3 x 10-15 cm2 and the broken curve presents the result obtained in the rough-sphere approximation used in [72, 80].

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... 

A similar defect is also inherent to the operator f(1), which rules the angular momentum relaxation according to... 

Burshtein A. I., Storozhev A. V. The angular momentum relaxation due to multiparticle collisions of molecules with atoms, Chem. Phys. 164, 47-55 (1992). 

Valiev-Ivanov model 219, 275 vibrational broadening 123 vibrational dephasing 111, 113-15, 123 vibrational relaxation, and angular momentum relaxation 92 vibrational transition, adiabatic dephasing 92... 

Specific values of r are helpful for identifying the nature of the scattering process. For example, if the momentum relaxation time is proportional to a given... 

In order to find the Green s function g, we consider the diffusive case when the Usadel equation is applicable. This equation can be used provided the condition Jr momentum relaxation time). Of course, this condition can hardly be satisfied for strong ferromagnets like Fe and in this case one should use a more general Eilenberger equation for a quantitative... 

FEMTOSECOND ELLIPSOMETRY A NEW TOOL FOR THE MEASUREMENT OF HOT ELECTRON MOMENTUM RELAXATION TIMES IN METALS... 

The measurement of hot electron momentum relaxation times in metals... 

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