Splitting phenomenon levels

The proof of Theorem 5.1.6 also rests upon the separatrix splitting phenomenon. To this end, one should represent the Kirchhoff equations as perturbations of integrable equations. Introduce a small parameter e replacing in the Kirchhoff equations e by ee. Then on the fixed four-dimensional level surface of two integrals... 

Figure 25 presents the homopolymer data in a scaled form. The splitting into Q-dependent plateau levels is much more pronounced than for PI, a phenomenon resulting from a faster relaxation rate and somewhat stronger constraints. Again, the Ronca model represents an excellent description of the experimental data reproducing the line shape, i.e. the relatively sharp crossover and the... 

The effect of intermolecular interactions can be readily observed when comparing the absorption spectrum of a molecule in solution to that in the solid state. In solution, where the molecules can be considered as isolated, the spectra are characterized by sharp lines corresponding to absorption bands. However, in the solid, intermolecular interactions cause the formation of exciton bands and splitting of the levels. This phenomenon is often referred to as Davydov splitting. This splitting is thus a measure of the strength of the interactions and for MOMs it can amount to 0.2-0.3 eV. 

In the absence of an external magnetic field, orbitally nondegenerate levels with spin multiplicity greater than 2 split due to direct electron spin—spin coupling (in first order) and spin—orbit coupling (in second and higher orders of perturbation theory). This phenomenon is called zero-field splitting (ZFS). The SH that describes this phenomenon can be formulated in... 

This phenomenon had been known for some time in the field of transition-metal complexes, but had not been exploited. A simple and possibly oversimplified view of why these forbidden transitions give rise to narrow fines is that the anisotropy found for Ams = +1 transitions stems from a marked dependence of the zero-field splitting upon orientation. Since this is primarily confined to a separation between the ms = 0 and ms = + 1 levels, the low-field Ams = + 2 transitions are unaffected, since the mB = 0 level is not involved (Fig. 156). 

Figure 16.1. (a) Simplified scheme of EPR phenomenon, showing the energy-level splitting (Zeeman effect) for the electron spin S = 1/2 (Ms = +1/2) as a function of applied magnetic field (H), (b) the EPR absorption line, and (c) first derivative of absorption line, indicating the g value and line width (AH), normally detected in the EPR spectra. 

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