Resonance values

Experimentally there are two alternatives. One is to fix the magnetic field that determines the Larmor frequency and to sweep the radiation frequency through this value. Alternatively radiation at a fixed frequency is used while the field sweeps through the resonance value. When the resonance condition is reached absorption of radiation occurs. 

As shown in the infrared absorbance spectrum of the condensation polymer (See Fig. 1), bands characteristic of absorbance of the urea resin at 3,400 cm-1, 3,000 cm-1, 1,680 cm-1, 1,540 cm-1, 1,380 cm-1, 1,100 cm-1, 1,020 cm-1, 780 cm-1, and characteristic absorbance of acrylami demethyl base at 800 cm-1 are present judging from this data, it is considered that N-methylacrylamide is connected with the end group of urea resin main chains and the imino group. The nuclear magnetic resonance (See Fig. 2) spectrum of the oligomer shows a resonance value of 6.48 ppm based on CH2= and a resonance value of 5.74 ppm based on -CH=. 

Two types of low resolution solid state NMR techniques can be distinguished a) broad line NMR in which the absorption signal is obtained by sweeping the magnetic induction B in the vicinity of the resonance value B0 (Eq. (1)), and b) pulsed techniques which are based on the possibility of rotating the magnetization under the influence of particular radiofrequency pulses, or pulse sequences. 

Another technique that can be used to determine the chemical nature of a thin film is infrared spectroscopy. Some materials will absorb certain frequencies in the infrared (wavelengths 2 to 25 microns) because of the excitation of vibrational energy transitions in molecular species. In the same way that electronic transitions in atoms can absorb radiation of specific frequencies, the vibration of a molecule (stretching or bending) will have a resonance value, and it will be excited by any radiation of this frequency. Consider the H20 molecule and its three vibrational modes, as shown in Figure 17. Clearly, each of these vibrational modes has its own resonant frequency, as indicated, and they are all in the infrared range. 

In the framework of the standard linear response theory, the relaxation times of precession are determined in the a< 1 limit according to the generic formula x = (ay//)-1. Setting the field equal to its resonance value, we get... 

Our last runs were with the (expensive) isotopic gas 13C1802 in our TEA laser system. We ran for some days with the diffracting grid set at 1 = 9.8595 urn (presumed resonance value), firing the laser with every other beam burst. During this period, the repetition rate of the AGS was 1.4 s. It is easy to see that a good quantity to look at to observe stimulated laser transitions is the ratio K /K. ... 

This expression includes only the terms due to a single frequency, but we can integrate over the range of frequencies concerned. Since the integrand in (6.299) makes a significant contribution only when v is near the resonance value vba we obtain the final result... 

Here Xo (2w), x (wiiw2) and Xo (O) are the non-resonant values of the hyperpolarisabilities. Thus second harmonic generation is resonantly enhanced at both the fundamental and the harmonic of the optical transition, sum and difference frequency generation at the fundamentals and the sum and difference frequencies, and the rarely observed optical rectification only at the fundamental frequency. The term 3 in the expansion gives rise to effects such as third harmonic generation, x(3) -3oj oj, oj,u>), electric field induced second harmonic generation, x(3) (- 2w 0,w, oj), the optical Kerr effect, x(3) (-oj oj, oj, -cj), etc. that will display resonances at oj, 2oj and 3u>. 

The complex factor in fr has a large negative real part near resonance for E < r and a large positive real part for E > Cr. The difference between the differential cross section and its non-resonant value has a rapid sign change at resonance. 

Because the choice of A2 — 1/2J for the decoupled, refocused INEPT experiment leads to completely refocused doublets, but antiphase triplets and quartets, this particular experiment with decoupling produces a subspectrum that contains only methinyl resonances. Values of A2 also can be selected to optimize the intensities of methylene and methyl resonances. The idea can be depicted graphically by defining an imaginary angle B =... 

Thus, subphthalocyanine 17 exhibits a large resonant third-order optical nonlinearity and fast response. The measured resonant third-order NLO response is two orders of magnitude larger than the off-resonant values of chloroboron subphthalocyanine, and of the same order of magnitude as the off-resonant values of polydiacetylene due to resonant enhancement. 

As J increases, the semimajor axis increases. Consequently the ratio n/n varies, and passes through resonant values. 

Notice that, except for the dependence on a, this series is formally similar to that giving the direct part of F. To complete the similarity, we can substitute for the factor a-1/2 with a power series expansion in the neighborhood of the exact resonant value and write it as... 

All N resonance values cited in this Section refer to an increase in shielding with respect to nitromethane as external standard.)... 

Assuming that the permittivity of metal Sm obeys e[ /id and jeml > e", the reflectivity Eq. 69 can be expanded around the resonant value of kz yielding a Lorentzian (with respect to kz) approximation of the reflectivity [6] ... 

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