Non-adiabatic Theories

From a mathematical perspective either of the two cases (correlated or non-correlated) considerably simplifies the situation [26]. Thus, it is not surprising that all non-adiabatic theories of rotational and orientational relaxation in gases are subdivided into two classes according to the type of collisions. Sack s model A [26], referred to as Langevin model in subsequent papers, falls into the first class (correlated or weak collisions process) [29, 30, 12]. The second class includes Gordon s extended diffusion model [8], [22] and Sack s model B [26], later considered as a non-correlated or strong collision process [29, 31, 32],... 

In NMR theory the analogue of the relation (1.57) connects the times of longitudinal (Ti) and transverse (T2) relaxation [39]. In the case of weak non-adiabatic interaction with a medium it turns out that T = Ti/2. This also happens in a harmonic oscillator [40, 41] and in any two-level system. However, if the system is perturbed by strong collisions then Ti = T2 as for y=0 [42], Thus in non-adiabatic theory these times differ by not more than a factor 2 regardless of the type of system, or the type of perturbation, which may be either impact or a continuous process. 

It is clear that J-diffusion is a good approximation for rotational relaxation as a whole, if the centre of equilibrium distribution over J is within the limits of non-adiabatic theory. In the opposite case m-diffusion is preferable. Consequently, the J-diffusion model is applicable, if the following inequality holds ... 

Fig. 5.6. Collisional broadening of N2 rotational components, (a) In Q-branch, calculated by purely non-adiabatic theory at 300 K (1) and with adiabatic corrections at 300 K (2) and at 100 K (3) [215]. (b) In S-branch, calculated in [191] with adiabatic corrections using the recipe of Eq. (5.56). The experimental data (+) are from [214].

The non-adiabatic theory indicates that electron - vibration (phonon) interaction, at stabilization (minimization) of the fermionic ground state... 

The vibrational adiabatic approximation is hardly justified because the reaction channel is curved. This means that motion along s couples with some vibrational modes, and also the vibrational modes couple among themselves. Therefore, we have to use the non-adiabatic theory, and this means that we need coupling coefficients B (p. 906). The Miller-Handy-Adams reaction path Hamiltonian theory gives the following expression for the Bkk (Fig. 14.7) ... 

The non-adiabatic theory for a diatomic (r denotes the electronic coordinates, R stands for the vector connecting nucleus b with nucleus a, R = R, A means the number of electrons, m is the electron mass, V represents the Coulombic interaction of all particles, p. is the reduced mass of the two nuclei of masses Ma and Mb). 

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