Weak oscillator

Van Gelder The Perl is not a normal oscillator. What we see in the cryptochromes is that Crj2 has an exaggerated phase response curve probably because the oscillator is not as robust. It may be the case that Perl is also a weak oscillator with an accordingly exaggerated phase response curve. 

In the probe area, where the sample is placed, resonance is obtained by superimposing a weak oscillating field B on the field B0 generated by a coil that is fed by an AC radiofrequency. In order for B to have the proper space orientation, the propagation axis of the radiofrequency has to be perpendicular to the Oz axis (Fig. 9.8). The transfer of energy from the source to the nuclei occurs when the radio-frequency of the source and the frequency of precession are the same. When this occurs, nuclei in energy state E can pass to energy state E2 the relative populations become modified. 

The Laporte rule states that transitions between states of the same parity, u or g, are forbidden i.e. u - g and g - u but g +-> g and u +-> u. This rule follows from the symmetry of the environment and the invoking of the Bom-Oppenheimer approximation, But since, due to vibrations, the environment will not always be strictly symmetrical, these forbidden transitions will in fact occur, though rather weakly (oscillator strengths of the order of 10 4). All the states of a transition-metal ion in an octahedral environment are g states, so that it will be these weak symmetry forbidden transitions (called d-d transitions) that will be of most interest to us when we study the spectra of octahedral complexes. 

Naively one could think that scattering on weak barriers cannot possibly yield a sharp peak in G(eo, T). Indeed, the transmission probability as a function of e does not have any peak at e = eo, in contrast to the case of resonant tunneling. At high T, G(eo,T) is a weakly oscillating (with a period A) function of eo- The only difference with the non-interacting case is an enhanced amplitude of the oscillations. In fact, however, the interaction-induced vanishing of the transmission probability at ep for T = 0 does lead to a narrow Lorentzian peak of G(eo,T), provided that T is low enough and the barriers are not too asymmetric. 

Weak oscillations Weak oscillations Weak oscillations ... 

A. Hemptinne subjected a large number of substances to rapid electric oscillations in an arrangement which, according to the method of Lecher,3 permitted an investigation of the influence of various wave lengths.4 He found that methyl alcohol 6 at 15 mm. pressure and with weak oscillations gave ... 

In Figure 6, we have plotted the differential methylene polarizability (the isotropic polarizability per methylene unit) of the n-alkanes. The most notable feature of this plot is the increase in the isotropic polarizability with the number of carbon atoms. From the decomposition of the polarizability along the principal directions in Figure 7 (with the Cartesian directions defined as for Figure 3), we note that the differential polarizability increases only in the x direction—that is, in the component parallel to the carbon chain. In the other two directions, the polarizability converges smoothly except for weak oscillations in the in-plane ayy component, oppositely directed to those in the other in-plane component axx. These oscillations, which are absent in the isotropic polarizability, may be linked to the alter-... 

For the weak oscillator the shapes of all graphs related to h and e are symmetrical with respect to the resonance frequency, pairwise similar, and no distinctive wavenumber shift is found. The reflectance spectrum resembles closely the dispersion anomaly of the (real) refractive index. The spectral variations of the components of the dielectric function are... 

Figure 6.4-6 Simulated spectra of a weak oscillator (strength/ = 0.8 10 cm ). Same notations as for Fig. 6.4-5.

The EXAFS spectra for Br" display weak oscillations, indicating either a small coordination number or a large disorder of the coordination bond lengths due to the weak Br -solvent interactions. Some of the spectra display strong multi-electron excitation structures and this structure had to be removed before the EXAFS analysis. The EXAFS oscillations for several typical solutions are given in Fig. 1. In all cases the oscillations for aprotic solutions arc weaker compared to aqueous or protic solutions. Most of the spectra could be analyzed by using a one-shell model, but it is clear that the data for acetic add (4) and t-butyl alcohol (12) can not be adequately analyzed by the one-shell model. 

Mq that is shrouded in the strong magnetic field Bq is too weak to be measured. So, to get a signal, resonance of the nuclei is obtained by superimposing upon 5q, in the probe area, a weak oscillating field which originates fi-om a coil that is fed with alternating current radiofrequency. 

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