Scalar irradiance

The rate of photolytic transformations in aquatic systems also depends on the intensity and spectral distribution of light in the medium (24). Light intensity decreases exponentially with depth. This fact, known as the Beer-Lambert law, can be stated mathematically as d(Eo)/dZ = -K(Eo), where Eo = photon scalar irradiance (photons/cm2/sec), Z = depth (m), and K = diffuse attenuation coefficient for irradiance (/m). The product of light intensity, chemical absorptivity, and reaction quantum yield, when integrated across the solar spectrum, yields a pseudo-first-order photochemical transformation rate constant. 

U represents the scalar irradiance, ex is the molar absorptivity (or molar extinction coefficient) of the chromophore, l is the light path length, and [P] is the concentration of the chromophore that initiates the photoreaction (e.g., the halocarbon itself, a natural substance, or a complex of the halocarbon with a natural substance). The rate of light absorption depends on the spectral overlap between the light source and the spectrum of the chromophore that initiates the photorcaction. 

In equation (9) p fi is the fraction of downwelling scalar irradiance contributed by downwelling cosine irradiance (Fd/Fo,d), measured just below the surface, and fib is the backscattered fraction of b. This relationship was developed for Case 1 waters (described in Section 2) and should be tested for validity in non-Case 1 waters. Other empirical relationships for predicting from lOPs are described in Kirk [6,10]. 

I. In reference to a spectral feature, the scalar or magnitude of that feature. 2. Chromatic purity. 3. The magnitude of a particular force or energy per unit (e.g., surface, charge, mass, time, volume, etc.). 4. Synonym for photon irradiance. 5. Synonym for fluence rate. 6. Synonym for irradiance illuminance. 7. Synonym for radiant power. 8. Symbohzed by /, synonym for radiant intensity. 9. See Magnetic Field Strength. 10. See Electric Field Strength. 

An amount of energy I a2 is removed from a beam with irradiance /, as a result of reflection, refraction, and absorption of the rays that are incident on the sphere that is, every ray is either absorbed or changes its direction and is therefore counted as having been removed from the incident beam. An opaque disk of radius a also removes an amount of energy I a2, and to the extent that scalar diffraction theory is valid, a sphere and an opaque disk have the same diffraction pattern. Therefore, for purposes of this analysis, we may replace the sphere by an opaque disk. 

If B2 is applied at resonance with the nuclei X to be decoupled, ot2jy cancels B0 so that Beff. = B2, as in eq. (1.33). As a result, the magnetization vectors of the irradiated nuclei X precess perpendicularly to B0. Now, the irradiated nuclei X have their spins quantized perpendicularly to B0, while the spins of the observed nuclei A are still quantized along B0. Since the observed coupling between nuclei A and X is the scalar product of the spin quantizations IA and /x [28-30], the observed coupling is related to the angle a enclosed by the spin quantizations /A and /x. 

The second approach is the use of the dynamic nuclear polarization (DNP) detection principle. Dorn and co-workers have pioneered the application of this technique [9,10], Whereas the NOE enhancement of 13C nuclei in the conventional 13C H recording is dependent upon the 7h/7c ratio (NOE = Th/ Tc = 2 1), the DNP enhancement relates to the ye/yuc ratio (2640 1). In an electron-nucleus spinsystem, the electron-electron transitions are saturated by microwave irradiation and magnetization transfer from electron to nucleus (Overhauser effect) occurs via a scalar and/or dipolar mechanism. The DNP enhancement, A, is described by the following equation ... 

In modem NMR, in order to obtain data on through-bond, scalar connectivities or through-space, dipolar connectivities between individual spins, double or multiple irradiation experiments are used. These rely on selective irradiation of a particular resonance line with a radio frequency field and observation of the resulting effects in the rest of the spectrum. With 2D ESR techniques as well as with 2D NMR techniques, limitations of one-dimentional methods connected with overlapping resonance have been overcome (Fig. 1.7). 

A ID NMR experiment provides information on the chemical shift and spin-spin coupling fine structure of the individual resonances in the spectrum. Double or multiple pulse irradiation experiments provide additional data on through bond scalar connectivities or through space dipolar connectivities, which relate to resonance assignments, conformational state and dynamics of the molecules under investigation. 

Under continuous uv irradiation, the observed steady-state polarization (whether by cw or by FT spectrometers) may be substantially modified by various nuclear relaxation processes. For example, Closs and Czeropski (35,36) have demonstrated that CIDNP can be transferred from a group of polarized nuclei to another group not originally polarized. Both the dipolar and the scalar relaxation mechanisms (of the nuclear Overhauser effects) can be operative. The extremely interesting case of intramolecular dipolar nuclear cross relaxation reported by Closs and Czeropski (35) involves the thermal reaction of... 

As demonstrated by Hartmann and Hahn (1962), energy-matched conditions can be created with the help of rf irradiation that generates matched effective fields (see Section IV). Although Hartmann and Hahn focused on applications in the solid state in their seminal paper, they also reported the first heteronuclear polarization-transfer experiments in the liquid state that were based on matched rf fields. A detailed analysis of heteronuclear Hartmann-Hahn transfer between scalar coupled spins was given by Muller and Ernst (1979) and by Chingas et al. (1981). Homonuclear Hartmann-Hahn transfer in liquids was first demonstrated by Braunschweiler and Ernst (1983). However, Hartmann-Hahn-type polarization-transfer experiments only found widespread application when robust multiple-pulse sequences for homonuclear and heteronuclear Hartmann-Hahn experiments became available (Bax and Davis, 1985b Shaka et al., 1988 Glaser and Drobny, 1990 Brown and Sanctuary, 1991 Ernst et al., 1991 Kadkhodaei et al., 1991) also see Sections X and XI). 

Chalcogenide glasses respond to irradiation with optical or ultraviolet photons in a unique manner. They exhibit photostructural effects. Photostructural effects, in general, fall into two different categories. The first category is based on changes in scalar properties. 

The 90°/90° SPT experiment can also be used to determine the individual coupling networks in a binary mixture. In Check it 5.2.4.5 the single line at 3.69 ppm is irradiated and all the signals of the spin system which are connected by scalar coupling to the irradiated line can be determined. 

There are a couple of special methods of separating the contribution of dipolar relaxation in solution. One is by the NOE factor which is the fractional difference in the signal intensity of one spin with and without irradiation applied to another spin system. For a sample containing protons and carbon-13 in the motionally narrowed limit, this factor should be 2 if the relaxation takes place through the dipolar and the scalar interactions. Thus, the departure from 2 of the NOE factor is an indication of other relaxation mechanisms. Clearly, any other pairs of spin systems with NOE s can be treated this way, with appropriate limiting NOE factors. See, for example, Noggle and Shirmer listed in Appendix A for more details. 

---