Relative line intensities

Fig. 3.6 (a) Decay scheme of and (b) ideal emission spectrum of Co diffused into rhodium metal. The nuclear levels in (a) are labeled with spin quantum numbers and lifetime. The dashed arrow up indicates the generation of Co by the reaction of Mn with accelerated deuterons (d in Y out). Line widths in (b) are arbitrarily set to be equal. The relative line intensities in (%) are given with respect to the 122-keV y-line. The weak line at 22 keV, marked with ( ), is an X-ray fluorescence line from rhodium and is specific for the actual source matrix... 

The anisotropic/factor may also manifest itself in the relative line intensities of Zeeman split hyperfine spectra in a poly crystalline absorber. Expanding f(0) in a power series... 

The line splittings together with the relative line intensities allowed us to position the organic cations in their respective frameworks. 

Table 5,9 Relative Line Intensities for Simple Multiplets...

In a related study, we have investigated the hfs proton resonances of Hb A, Hb F, Hb Zurich (p63His —> Arg), and Mb, all in the azidomet form in 0.1 M phosphate in D20 at pH 6.9 and 31°C, as shown in Fig. 35 (Davis et al., 1969b). The prominent lines from +15 to +23 ppm downfield from HDO in these spectra have been assigned to some of the methyls of the porphyrin on the basis of relative line intensities and comparison with the NMR spectra of met-MbN3... 

One can explore what functions of each parameter matrix are actually obtainable by scientists using the above spin-Hamiltonian, via the measurable line positions and relative line intensities of magnetic-resonance spectra see publications by Skinner and Weil130 154 for some aspects of this. The question as to which parameter matrices occurring in Equation (A3) are directly available from experimental data is far from trivial7 26 matrices g, gn and A are not, while their squares (see below) are. 

There is a fundamental difference between the operation of a powder camera and a diffractometer. In a camera, all diffraction lines are recorded simultaneously, and variations in the intensity of the incident x-ray beam during the exposure can have no effect on relative line intensities. On the other hand, with a diffractometer, diffraction lines are recorded one after the other, and it is therefore imperative to keep the incident-beam intensity constant when relative line intensities must be measured accurately. Since the usual variations in line voltage are quite appreciable, the x-ray tube circuit of a diffractometer must include a voltage stabilizer and a tube-current stabilizer. 

The observed values of sin 0 for the first 16 lines are listed in Table 10-5, together with the visually estimated relative line intensities. This pattern can be indexed on the basis of a cubic unit cell, and the indices of the observed lines are given in the table. The lattice parameter, calculated from the sin 6 value for the highest-angle line, is 6.46 A. 

Identification of the unknown begins with making its diffraction pattern. Sample preparation should result in fine grain size and in a minimum of preferred orientation, which can cause relative line intensities to differ markedly from their normal values. Note also that relative line intensities depend to some extent on wavelength this should be kept in mind if the observed pattern is compared with one in the data file made with a different wavelength. Most of the patterns in the file were made with Cu Ka. radiation, except those for iron-bearing substances. 

The derivation of this equation can be found in various advanced texts, for example, those of Warren [G.30] and James [G.7]. It applies to a polycrystalline specimen, made up of randomly oriented grains, in the form of a flat plate of effectively infinite thickness, making equal angles with the incident and diffracted beams and completely filling the incident beam at all angles 6. The second factor in square brackets, containing F, p, and 0, will be recognized as Eq. (4-19), the approximate equation for relative line intensities in a Debye-Scherrer pattern. 

It displays a superposition of lines that correspond to the excitation of different numbers of vibrational quanta during the electronic transition (hence the name multiphonon transition rate). The relative line intensities are determined by the corresponding Franck-Condon factors. The fact that the lines appear as <5 functions results from using perturbation theory in the derivation of this expression. In reality each line will be broadened and simplest theory (see Section 9.3) yields a Lorentzian lineshape. 

Fig. 17. Relative line intensity R (see Table III and text) versus angle

The relative line intensity R of a quadrupole split spectrum is determined by the angle 0 between y and the principal axis of the electric field gradient z = Vzz- From Eqs. (3) and (4) and assuming the assymmetry parameter rj to be zero, the intensity ratio R of the two absorption fines of the quadrupole split Mb single crystal spectrum is derived to be ... 

Another nonlinear technique that is potentially applicable to thermometric measurements is DPWM [7,9]. Por instance, a Boltzmann plot constructed out of the relative line intensities of a DPWM spectrum can lead to temperature predictions that can be as accurate as CARS in some cases. An alternative method is to fit theoretical simulations to the experimental spectrum. Nonetheless, the versatility of CARS is not equaled by DPWM. In effect, single pulse measurements seems to be limited to some radical species and mode fluctuations of conventional lasers perturb the data severely. To avoid troubles with such laser intensity fluctuations, saturated DPWM is often employed, but the difficulties of spectral S5mthe-sis remain a serious hindrance to a major role of DPWM thermometry. 

All that remains now is to relate the relative line intensities to the total absorption intensity. The equations for the resonant cross-section of a single peak in Section 1 are still basically valid except that the term for each hyper-fine line must additionally contain the appropriate... 

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