Relaxation phenomena definitions

For reproducing as closely as possible diabatic conditions, we have fixed the Cl—Cl bondlength at its neutral equilibrium value. This way, the system depends on two parameters as shown in Figure 1. Previous experimental and theoretical studies on similar systems, [1,18] have shown that electron jump from Li to the acceptor molecule CI2, which has, once relaxed, a positive vertical electron affinity (see Table 1), is likely to take place at a distance d, (see the definition of this parameter in Figure 1) which is superior to the LiCl equilibrium distance (MP2 value 2.0425 A). The description of this phenomenon in terms of MO and states will be briefly recalled in the next section. 

A phenomenon closely related to electronic relaxation is the existence of diffuseness in the absorption spectra of the higher excited electronic states of molecules. It has been known for some time that very fast electronic relaxation processes occur when the higher excited states of molecules are caused to interact with radiation. It is remarkable then that only in relatively recent work has the association between these fast processes and spectral diffuseness been clearly focused upon. These spectral results provide some of the most definitive features that may be associated with the electronic relaxation mechanisms. First, the results from solid-state spectra 62 ... 

Classically, the experimental curve interpretation is often limited to the definition of a distribution function in which the Debye-type relaxation superposition is accounted for by two parameters a and jS. From this description, we learn nothing about the physical processes involved this is often the relaxation frequency zone which permits connection of the observed evolutions to a particular polarisation phenomenon. Moreover, for materials with large free carrier concentration, the conduction and polarisation effects are separated in an arbitrary way, assuming that the contribution to the conduction phenomena is limited to a term e" conduction = (Tdc/cyto over the whole frequency range. 

The set of approximations leading to Eq. 3.33 is often summarized as the sudden approximation. The thumb rule described above concerns an independent particle description of the shake phenomenon. With this description one can thus associate each pair of occupied and unoccupied orbital indices to two specific shake-up states, a triplet and a singlet parent coupled state. Systems that can be described this way receive shake intensity through the effect of orbital relaxation — the more relaxation the more intensity. The effect of relaxation on intensities is clearly also seen from the overlap element in Eq. 3.33. However, in order to obtain quantitative prediction for shake-up intensities, more sophisticated models, including the effect of electron correlation, must be considered. With the definition of correlation energy as the difference between one-determinant, Hartree-Fock, energy and the exact expectation value of the electronic nonrelativistic Hamiltonian, final-state correlation is always... 

To simulate the viscoelastic flow, the Oldroyd-B model has been implemented in the VOF-code. Stabilization approaches, such as the Positive Definiteness Preserving Scheme and the Log-Conformation Representation approach have been adapted and implemented in the code to stabilize the simulations at high Weissenberg numbers. The collision of viscoelastic droplets behaves as an oscillation process. The amplitude of the oscillation increases and the oscillation frequency decreases when the Deborah number becomes larger. The phenomenon can be explained with the dilute solution theory with Hookean dumbbell models. An increase of the fluid relaxation time yields a decrease of the stiffness of the spring in the dumbbell and restrains the deformation of the droplets. In addition, with larger the viscosity ratio the collision process is more similar to the Newtonian one since the fluid has less portion of polymers. 

Another behaviour which leads to the definition of multiple relaxation times in the case of dipole-dipole relaxation of identical spins is the so-called cross-correlation phenomenon. Eq. 17 is applicable for two identical interacting nuclei. What happens in the case of, let us say, four identical nuclei placed at... 

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