Splitting in the magnetic field

The presence of the magnetic field is covered by the following form of the Hamiltonian 

The matrices for individual spin components are presented in Appendix 2. Then the energy levels are obtained as eigenvalues of the secular equation 

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Every term is tlms split up into 2k -h 1 terms by the magnetic field. It is therefore to be expected that the spectral lines also possess the property of splitting in the magnetic field. That this is actually... 

EPR spectra of ZrSi04 Cr contain a single line with g = 1.986, g = 1.956 which is characterized by D2d local symmetry (K = 1). ion has spin S = 1/2 and with any symmetry of the crystal field, splitting in the magnetic field always leads to the appearance of a single line in the EPR spectrum. The possible connection of the line with Cr is confirmed by its intensity correlation with Cr concentration in the melt. The ratio of the main values of g-tensor is characteristic for Cr + (3d configuration) in tetrahedral coordination (Krasnobayev et al. 1988). 

Energy level splitting in a magnetic field is called the Zeeman effect, and the Hamiltonian of eqn (1.1) is sometimes referred to as the electron Zeeman Hamiltonian. Technically, the energy of a... 

In 1925, Wolfgang Pauli gave chemists what they wanted from the physicists a physical principle underlying electron-pair valency. Pauli built on the fact that in addition to the continuous, line, and band spectra, there is a fine structure of doublets, triplets, and multiple lines, some of which are split in a magnetic field (Zeeman effect). 

Figure 8-10 2H NMR spectra of dimyristoyl phosphatidyl-cholme-d27/water in lamellar phases at 40°C. One chain of the phosphatidylcholine is fully deuterated, containing 27 atoms of 2H. The mole ratios of water to lipid were 5.0 in (A) and 25.0 in (B). The average interfacial areas per alkyl chain as measured hy X-ray diffraction were 0.252 nm2 for (A) and 0.313 nm2 for (B). 2H NMR spectra are presented as "powder patterns" because the lipid molecules are randomly oriented in the magnetic field of the spectrometer as if in a powder. This gives rise to pairs of peaks symmetrically located on both sides of the origin. The separation distances are a measure of the quadrupole splitting of the NMR absorption line caused by the 2H nucleus. The various splittings of the resonances of the 13 -CH2- and one -CH3 groups reflect differences in mobility.109 The peaks have been assigned tentatively as indicated. From Boden, Jones, and Sixl.115 Courtesy of N. Boden.

Fig. 1.16. The splitting of the S = V2 manifold in a magnetic field Bg when (A) g is isotropic and there are only two energy values independent of the orientation of the molecule in the magnetic field and (B,C) the energies depend on the orientation of the molecule in the magnetic field (A , > A l).

Figure 7.7 Fast but anisotropic segmental motion results in a solid-like contribution to the NMR signal. This contribution is expressed in terms of a fractional contribution q of the second moment M2 of the rigid lattice line of a single chain or residual dipolar interactions between protons. The line splitting caused by the dipole-dipole interaction depends on the orientation angle q of the internuclear vector of the coupling protons in the magnetic field B(). The distribution of orientation angles changes with the...

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