The relative intensities of hyperfine lines

Table 5.5.2. Binomial coefficients for the relative intensities of hyperfine lines (spin = 1/2)...

Things get a little more complicated when a spin 1 nucleus like 14N is added to the picture, but the same technique works again for the determination of the relative intensities of the ESR lines. Consider, for example, the relative intensities of the hyperfine lines arising from the pyrazine anion radical, whose spectrum is shown in Figure 2.3. Like that of the naphthalene anion radical, the spectrum observed for the pyrazine anion radical2 consists of 25 well-resolved... 

Fig. 20. Dependence on temperature of the resolved hyperfine-shifted resonances of ferricytochrome c. The numbers on the right give the relative intensities of the lines...

Regarding the relative intensities of the observed spin polarization mechanisms, it is also important to note that the [3-hyperfine interactions in these radicals are conformationally modulated, and this process can also quench RPM polarization. In a qualitative way, we can consider the modulation process to be a relaxation mechanism that exchanges magnetization between different nuclear spin orientations. Since these different orientations can have opposite phases of RPM polarization, the exchange of emissive and absorptive lines can cancel the intensity of the transitions. 

Fig. 3.7 Curves illustrating the changes in the relative intensity of two hyperfine lines caused by saturation effects (a) with change in recoilless fraction, (b) with change in absorber thickness.

Hyperfine interactions due to ring atoms are also observed in the hf ODMR spectra of triplet benzophenones (Mucha and Pratt, 1976, 1977a). For example. Fig. 10 shows some representative spectra taken in two principal axis orientations of (nre ) 4,4 -difluorobenzophenone (DFBP). With H z, a 1 2 1 pattern is observed with a splitting of 9 G, which is consistent with a hyperfine interaction involving two equivalent F (/ = ) nuclei. The relative intensities of the two lines denoted by asterisks are found to be power dependent thus, these lines are probably forbidden in character. In the H x orientation, the Airis = 1 transitions also exhibit a 1 2 1 pattern with a splitting of 18 G in the low-field line. No F hyperfine structure is resolved with H y. These data may be interpreted to yield the estimate > 0.10 for the rr-orbital spin densities of the para ring carbons in DFBP. 

The relative intensities of the lines in a Mossbauer spectrum provide additional information about the orientation of the hyperfine fields with respect to the crystal system in the case of single crystals or partially oriented (textured) samples. For pure magnetic or electric hyperfine fields the intensities are analytical expressions dependent on the direction of the fields with respect to the direction of y-radiation. For powder samples the intensity ratios of pure transitions do not depend on the strength of the fields. 

While the methods discussed above may provide a good fit to the observed spectra, they typically need to be provided with mean values for the isomer shift and quadrupole splitting and with relative intensities for the outer, middle and inner pairs of lines in the magnetically split sextet spectrum. A different value for these relative intensities will often lead to an equally good fit to the Mossbauer spectrum, with a different, compensating distribution of the hyperfine field. Thus these analyses do not provide a sensitive and reliable method of determining the relative intensities of the... 

Magnetic structure determinations In certain cases details of the magnetic structure can be elucidated from hyperfine interaction measurements. For example, in Mbssbauer effect experiments employing single crystal absorbers, the relative intensities of the component lines of the spectrum depend on the angle between the gamma ray quantum and the hyperfine field at the nucleus. The latter is in turn parallel to the ionic moment. By such an experiment, Reese and... 

Fig. 48. Temperature dependence of the magnetic hyperfine field (in T) for NpCujSij. In the shaded region both a single line and a split pattern appear. The relative intensity of the single-line pattern diminishes with lower temperature and vanishes around 31 K. The dashed line gives the Np " free-ion field. [Taken from Kalvius et al. (1985).]...

Fig. 10.86. (a) Energy level diagram showing hyperfine splitting for a free electron by nucleus of spin = proton) (b) first derivative line (c) second derivative (d) Stick plot of a first derivative line—the relative intensities of the lines in a derivative spectrum are shown by the heights of the lines in the diagram. AH is the hyperfine splitting constant. 

Much larger differences of populations between the different hyperfine levels can be created by suitably altering the relative intensities of the hyperfine components of the pumping lamp. Since these components are very close together conventional interference filters cannot be used, but fortunately in many cases the natural displacement between the resonance lines of different isotopes of an element enables selective light sources to be constructed. This is especially true in mercury, as shown by Table 16.1, and in the case of rubidium which we consider now. 

Most Mossbauer spectra are split because of the hyperfine interaction of the absorber (or source) nuclei with their electron shell and chemical environment which lifts the degeneracy of the nuclear states. If the hyperfine interaction is static with respect to the nuclear lifetime, the Mossbauer spectrum is a superposition of separate lines (i), according to the number of possible transitions. Each line has its own effective thickness t i), which is a fraction of the total thickness, determined by the relative intensity W of the lines, such that t i) = Wit. 

Fig. 7.53 Transmission Mossbauer spectra of the 137, 155, and 187 keV nuclear transitions of 186,188,190qj taken with sources emitting an unsplit line and (a) Os02-absorber (rj 0), (b) OSP2-absorber (rj 0.74). The curves are the results of least-squares fits. The vertical bars indicate the positions and relative intensities of the individual hyperfine components (from [254])...

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