Nucleus hyperfine structure experiments

The electron magnetic moment may also interact with the local magnetic fields of the nuclear dipole moments of nuclei around it. A single electron centered on a nucleus of spin I will experience 2/ -f 1 different local magnetic fields due to the 27 - - 1 different orientations of the nuclear spin I in the external magnetic field. This interaction, which is of the order of 10 cm. i, causes a hyperfine structure in the EPR spectrum. This structure is further discussed and illustrated in Section III,B. 

The hyperfine structure constants of T1 6p[y2 Tl + which (like X and M) depend on operators concentrated near the T1 nucleus, were also calculated. The errors in the DF values are 10-15% with respect to experiment and the RCC-SD results are within 1-4% of experiment. The improvement in X and M upon inclusion of correlation is expected to be similar. 

The hyperfine structure interval in hydrogen is known experimentally on a level of accuracy of one part in 1012, while the theory is of only the 10 ppm level [9]. In contrast to this, the muonium hfs interval [12] is measured and calculated for the ground state with about the same precision and the crucial comparison between theory and experiment is on a level of accuracy of few parts in 107. Recoil effects are more important in muonium (the electron to nucleus mass ratio m/M is about 1/200 in muonium, while it is 1/2000 in hydrogen) and they are clearly seen experimentally. A crucial experimental problem is an accurate determination of the muon mass (magnetic moment) [12], while the theoretical problem is a calculation of fourth order corrections (a(Za)2m/M and (Za)3m/M) [11]. 

There are also pulse EPR methods that probe the chemical or rather magnetic environment. These are pulse electron nuclear double resonance (ENDOR) and hyperfine sublevel correlation (HYSCORE) spectroscopy, which allow measuring hyperfine couplings from the unpaired electron spin to surrounding magnetically active nuclei ([20] in Fig. 3 this is a P nucleus). As these experiments are performed in frozen solution (e.g., in all examples of this chapter) or in solids, from the anisotropy and orientation dependence of the hyperfine coupling one can obtain valuable information on the structure up to 1 nm. 

Special TRIPLE [2] can give the number of equivalent / = Vi nuclei. The two RF-frequencies are swept to simultaneously correspond to the two ENDOR transitions for the same nucleus, Fig. 2.4(c). The method is employed particularly to radicals in liquids showing hyperfine structure due to H nuclei. The method is more sensitive than the usual ENDOR experiment. The theoretical background is described in original [2] and review literature [15, 16]. 

The first term results from the Fermi contact interaction, while the second represents the long-range dipole-dipole interaction. In the equations above, ge is the free-electron g factor, /Xe the Bohr magneton, gi the nuclear gyromagnetic ratio, and /xi the nuclear moment. Moreover, the nucleus is located at position R, and the vector r has the nuclear position as its origin. Finally, p (r) = p (r) — p (r) is the electron spin density. The only nontrivial input into these equations is precisely this last quantity, i.e. Ps(r), which can be computed in the LSDA or another DFT approximation. The resulting Hamiltonian can be used to interpret the hyperfine structure measured in experiments. A recent application to metal clusters is reported in Ref. [118]. 

Chemical bonds can have covalent character, and EPR spectroscopy is an excellent tool to study covalency An unpaired electron can be delocalized over several atoms of a molecular structure, and so its spin S can interact with the nuclear spins /, of all these atoms. These interactions are independent and thus afford additive hyperfine patterns. An unpaired electron on a Cu2+ ion (S = 1/2) experiences an / = 3/2 from the copper nucleus resulting in a fourfold split of the EPR resonance. If the Cu is coordinated by a... 

Mossbauer hyperfine spectra are useful in the determination of nuclear parameters, especially those of the excited states. Their significance stems from the fact that the structure of the nucleus is still poorly understood. Comparison of the parameters as measured with the values estimated from theory is used to discover the validity or inadequacy of the nuclear model. The rare-earth elements are popular for this type of work because of the proliferation of Mossbauer resonances, making it feasible to study the effects of successive proton or neutron addition over a range of nuclei. Although theory and experiment are sometimes in accord, gross differences are not unusual. 

More elaborate pulse sequences have been designed to selectively extract specific information about a spin system. A particularly useful experiment for structural studies of metal complexes is the two-dimensional four-pulse experiment called HYSCORE, hyperfine sublevel correlation spectroscopy. The resulting two-dimensional plot reveals the correlation between different modulation frequencies arising from the same nucleus, which greatly facilitates assignment of frequencies in complicated spin systems. ... 

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... 

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