Nonadiabatic region

In the nonadiabatic regime A is proportional to the adiabatic splitting 2 Fd. The instanton trajectory crosses the barrier twice, each time bringing the factor A/A a associated with the probability to cross the nonadiabaticity region remaining on the same adiabatic term (and thus... 

The pair correlation function of the velocities and the pair correlation functions of some time derivatives of the velocity are sometimes taken into account.75 However, the validity of this description in the nonadiabaticity regions also has to be proved. The dynamic description or the description using the differentiable random process is more rigorous in this region.76... 

However, if the region of nonadiabatic behavior is well localized in M, the classical treatment of the nuclear subsystem can be preserved and the evolution of the polyatomic system in the nonadiabatic region (where no potential energy surface is defined ) is to be described by special means. 

The real part Rt of Rc corresponds to the center of the nonadiabatic region. From equation (34) we get... 

Since the Coriolis coupling is largest at the distance of closest approach, the nonadiabatic region is localized near the turning point of the radial motion. In this region, close to R2, the two parallel terms A 2II1/2 and A n3/2 are approximated by exponential functions exp and the... 

Thus, the intramultiplet mixing in heavy alkalies can be accounted for by transitions in two nonadiabaticity regions that give competing contributions to the mixing cross sections. It seems clear now that an attempt [62] to interrelate experimental data resorting only to equation (57) cannot be justified. 

Nonresonant excitation transfer, that is, intramultiplet mixing, requires discussion of possible nonadiabatic regions. As seen from Figure 5.8 there are several pseudocrossings, crossings, and mergings, but selection rules... 

Figure 9.12. Reaction sink W W 2 in our notation) as a function of the reaction coordinate X in the classical limit. = V lhE . The parameter W is defined in terms of the stationary reaction flux j X) as follows j X) = (j> (X) W(X), where (l) (X) is the equilibrium distribution function in the initial state. The parameter is the size of the nonadiabatic region ( a in our notation). (Reproduced from [114] with permission. Copyright (1999) by the American Institute of Physics.)...

Another basic theory of nonadiabatic transitions is the semiclassical Ehrenfest theory (SET). Although it can cope with multidimensional nonadiabatic electronic-state mixing, it inevitably produces a nuclear path that runs on an averaged potential energy surface after having passed across the nonadiabatic region, which is totally unphysical. Unfortunately, since SET seems intuitively correct, a naive and conventional derivation of this theory obscures how this critical difficulty arises. 

Then in Chap. 5, we show that nonadiabatic transition and the associated wavepacket bifurcation are never a product of mathematical imagination but can be indeed observed experimentally. The direct observation of the instant of nonadiabatic transition (namely, the passage of a wavepacket across a nonadiabatic region) has been achieved only recently. This chapter also discuss a possible control of nonadiabatic transitions on the basis of the notion of wavepacket bifurcation. 

Subsequently our characteristic way of discussion on nonadiabatic transition enters, paying a particular attention to the direct (experimental) observation of the nuclear wavepacket bifurcation in the passage of nonadiabatic regions. We show that the instant of nonadiabatic transition... 

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