Hyperfine nuclear spin quantum number

Equation (2.3) describes line positions correctly for spectra with small hyperfine coupling to two or more nuclei provided that the nuclei are not magnetically equivalent. When two or more nuclei are completely equivalent, i.e., both instantaneously equivalent and equivalent over a time average, then the nuclear spins should be described in terms of the total nuclear spin quantum numbers I and mT rather than the individual /, and mn. In this coupled representation , the degeneracies of some multiplet lines are lifted when second-order shifts are included. This can lead to extra lines and/or asymmetric line shapes. The effect was first observed in the spectrum of the methyl radical, CH3, produced by... 

Group 3 (Sc, Y, La) metallofullerenes exhibit ESR hfs, which provides us with important information on the electronic structures of the metallofullerenes. Typical ESR-active monometallofullerenes are La Cs2, Y Cs2, and Sc C82- The ESR hfs of a metallofullerene was first observed in La Cs2 by the IBM Almaden group (Johnson et al., 1992) (Eigure 15) and was discussed within the framework of an intrafullerene electron transfer. The observation of eight equally spaced lines provides evidence of isotropic electron-nuclear hyperfine coupling (hfc) to La with a nuclear spin quantum number I = 7/2. The observed electron g-value of 2.0010, close to that measured for the Ceo radical anion (Allemand et al., 1991 Krusic et al., 1991), indicates that a single unpaired electron resides in the LUMO of the carbon cage. They also observed hyperfine... 

The magnetic hyperfine splitting (MHS) depends on the nuclear spin quantum numbers and /g of the excited and ground state of the Mossbauer nucleus and on the effective magnetic field at the Mossbauer nucleus, which includes contributions from the local electronic spin, from the orbital momentum, from dipole terms, and from external fields. 

The excited-state nuclear spin quantum number can be determined from the hyperfine spectrum, but this parameter is usually known before a Mossbauer experiment is attempted with an isotope. 

In addition to the information available from g-values, we can obtain information about nuclei with nuclear spin quantum number / 0 which are close to the paramagnetic centre. The spins of such nuclei interact magnetically with the unpaired electron and give rise to a hyperfine interaction. There is a direct analogy here with coupling of nuclear spins in NMR spectroscopy. The hyperfine interaction is added to... 

The nuclear spin quantum number of excited state can be derived from the hyperfine spectra, but this is usually known before the Mossbauer experiment. 

If the interaction of an electron with a magnetic field were the only effect operative, then all ESR spectra of free radicals would consist of one line. When the nuclear spin quantum number / is nonzero a nuclear hyperfine interaction A is observed. When several equivalent nuclei are present (e.g., -CHs, -C.Hs), the number of lines in the spectrum is given by n,(2n-,li + ). where n is the number of magnetically equivalent nuclei /. 

At intermediate rates of rotation, the spectrum is not quite simple. The widths of the respective resonance lines depend not only on the hyperfine splitting constants a and a but also on the nuclear spin quantum numbers m and m, each given by... 

Figure 5 shows the hypothetical spectra of a free radical having two sets of two protons which exchange at slow, intermediate, and fast rates. At a slow rate, the observed ESR spectrum has a triplet of triplets due to the two sets of two protons. At an intermediate rate, no broadening occurs in the lines whose positions are either determined from the hyperfine splitting caused by the two sets with the same nuclear spin quantum number (m, = 2 or —2 and then m — nig = 0) or correspond to the special condition m = mg = 0. Other lines are broadened to varying extents, depending on the nuclear spin quantum number. At a fast rate, the observed spectrum is... 

The interaction of the unpaired electron with the nucleus splits the electron energy levels, generating a structure called spectral hyperfine structure or hf splitting (Poole, 1967). Each "Ms state" being split into a closely spaced group of (2/ + 1) levels (Orton, 1968). / is the nuclear spin quantum number. The way in which these give rise to hyperfine splitting of the resonance lines is illustrated in Fig. 3. 

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