Hyperfine components

Figure 5.12 shows the J= — 0 transition of the linear molecule cyanodiacetylene (H—C=C—C=C—C=N) observed in emission in Sagittarius B2 (Figure 5.4 shows part of the absorption spectrum in the laboratory). The three hyperfine components into which the transition is split are due to interaction between the rotational angular momentum and the nuclear spin of the nucleus for which 1= 1 (see Table 1.3). The vertical scale is a measure of the change of the temperature of the antenna due to the received signal. 

Very thick absorbers may be required for applied-field measurements to achieve reasonable absorption depths and measuring times because the Mossbauer spectra are usually split into several hyperfine components. Here the iron content may be as large as 100 pg Fe per cm (1.75 pmol Fe per cm ), which would correspond to t 1 for a two-line spectrum. For smdies of frozen solutions, Fe concentrations of 1 mM are desirable for each nonequivalent iron site [35]. 

From (4.56) and Table 4.3, we derive the relative intensity ratios 3 2 1 1 2 3 for the hyperfine components of a Zeeman pattern of a powder sample. The transition probability for the case of the polar angle 6 = Oq can readly be calculated by integrating (4.56) only over the azimuthal angle (j). One obtains a factor (1 + cos 0o)/2 and sin 0o for m = 1 and m = 0, respectively, which are multiplied by the square of the Clebsch-Gordan coefficients. As a consequence of the angular correlation of the transition probabilities the second and fifth hyperfine components (Fig. 4.17) disappear if the direction k of the y-rays and the magnetic field H are parallel (0q = 0). 

With h 6) - 1/sin 0)5(0 — Oq), one obtains the same result as given by (4.58), which implies that the anisotropy of the/factor cannot be derived from the intensity ratio of the two hyperfine components in the case of a single crystal. It can, however, be evaluated from the absolute/value of each hyperfine component. However, for a poly-crystalline absorber (0(0) = 1), (4.66) leads to an asymmetry in the quadrupole split Mossbauer spectrum. The ratio of l-Jh, as a function of the difference of the mean square amplitudes of the atomic vibration parallel and perpendicular to the y-ray propagation, is given in Fig. 4.19. 

The isotope is almost exclusively used for the investigation of chemical compounds. The resolving power of Mossbauer spectroscopy is demonstrated by the spectra from WS2 powder and single-crystal measurements as shown in Fig. 7.48 (from [222]). On the right-hand side of the picture, the angular dependence of E2 transitions for Aw = 2, 1,0 hyperfine components is indicated. 

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])...

Konovalova, T. A., S. A. Dikanov et al. (2001a). Detection of anisotropic hyperfine components of chemically prepared carotenoid radical cations ID and 2D ESEEM and pulsed ENDOR study.. /. Phys. Chem. B 105 8361-8368. 

Careful examination of the isotropic ESR spectra of organic radicals may reveal variations in line widths from one hyperfine component to another. Such effects... 

Upon y-irradiation of 1 in a CF3CCI3 matrix at 77 K [78], a radical cation was formed, the ESR spectrum of which consisted of nine broad hyperfine components spaced by ca. 0.75 mT (g = 2.0029 0.002), and the corresponding proton END OR spectrum exhibited two essentially isotropic signals at 25.83 and 24.58 MHz. The detailed analysis of the ESR and END OR spectra disclosed that the initially formed radical cation 1+ had transformed into the tetramethyleneethane radical cation 94+ (Scheme 17). In CFCI3 and CF2CICFCI2 matrices 1+ persists up to 100 K [79]. On going from 1 to l+, the set of eight equivalent protons splits... 

The frequency differences between ESR hyperfine components are much greater than NMR spin-spin splittings, so that the N14 quadrupole moment does not give line broadening in ESR spectra. 

Often a radical is deuterated to aid in the assignment of coupling constants. Deuterium has / = 1 and a much smaller gN value than the proton. Thus replacement of an H1 nucleus by H2 changes both the number of hyperfine components and their spacings. 

Displacements of the Hyperfine Components of the 2537-A. Resonance Line of Mercury from the X200 Component in cm. 1 X 103 Hyperfine References... 

The displacements of these hyperfine components (hfe) from the central X200 life are listed in Table II. 

Intensity Kilties of die Hyperfine Components to the X202 Line... 

Assuming four water molecules to be coordinated to the 0 ions, eight protons can interact with the unpaired electron of T . Nuclear hyperfine interaction with eight equivalent protons should result in nine hyperfine components with an intensity distribution of 1 8 28 56 70 -... 

The selection rules state that the total angular momentum quantum number may change by 1 or 0. Thus an element with several isotopes each with its own nuclear spin will present a line spectrum with a very complex and, under most experimental conditions, unresolved hyperfine structure. Nevertheless, as we shall see later, the overlap between the hyperfine components of a spectrum line is sufficiently incomplete to permit preferential excitation of one isotope in a mixture of isotopes by radiation from a lamp containing that same isotope. 

Further progress was made with very simple radicals, when Matheson and Smaller succeeded in resolving all the hyperfine components of the spectrum of ethyl radicals (Matheson and Smaller, 1958), thus confirming that the original six-line spectrum found by Gordy et al. (1955) was due to trapped ethyl radicals for which the lines were broad so that the small differences between a- and /3- protons were not resolved. 

In addition to the main hyperfine components discussed above, weak satellite lines are frequently detected, which correspond to transitions normally considered to be forbidden. Under certain circumstances the selection rule, that there is no change in orientation of the nuclear spin as the electron spin changes, breaks down, and simultaneous electron-nuclear transitions can occur. These are especially strong if the electron-nuclear coupling is very anisotropic and is comparable in magnitude to the direct interaction between the external field and the nucleus, which will, in general, have a different direction from that of the anisotropic interaction. Under these conditions the nucleus is affected by both fields, and quantum restrictions break down. 

Occasionally such intermolecular effects are specific and have sufficient lifetime to contribute individually to the spectrum. This is the case, for example, when organic radical-anions are studied in solvents of low ionizing power such as tetrahydrofuran. Ion-pairing then becomes important and, when alkali-metal cations are involved, the effect on the spectrum is to split each hyperfine component into four lines, each having one-quarter of the original intensity. This may convert a complicated spectrum into one that is quite uninterpretable, and can be avoided by using a better solvent or non-magnetic cation. However, it also provides evidence that contact ion-pairs are important in such solutions, and yields structural details unobtainable by other techniques. 

Fig. 6. Experimental spectrum of 127l2 shown with calculated hyperfine components a4-al8 of the R(67) 5-5 transition at 656 nm. The a4 component is offset by about 1 GHz from one quarter of the He+ 2S-3S transition frequency...

Fig. 6. Direct absorption, AM and FM spectra of the hyperfine components of the B-X R,(34)27-0 transition of I2 at 541 nm. Note the hyperfine Lamb-dips are observed in the absorption spectrum...

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