Spin gyromagnetic factor

GIAO (p. 786) gyromagnetic factor (p. 757) Hellmann-Feynman theorem (p. 722) homogeneous electric field (p. 731) intermediate spin-spin couphng (p. 768) linear response (p. 732) local field (p. 719)... 

An elementary particle has a magnetic dipole moment M proportional to its spin angular momentum I, i.e. M = yl, where y stands for what is called the gyromagnetic factor (characteristic for the kind of particle). 

The additional term SAI results in an EPR spectrum that is more complicated than those illustrated in Fig. 4.27. The EPR spectrum of one line (as for a scalar gyromagnetic factor) is split and the number of lines in the hyperfine pattern is given by 2m/- - 1, where n is the number of equivalent nuclei with spin quantum number I (compare this with eq. 4.15). For example, cobalt possesses one isotope, Co, with 7=. An unpaired electron on a Co " " centre couples to the Co nucleus giving rise to an 8-line splitting pattern (Fig. 4.28a). Many elements possess more than one isotope (see Appendix 5). For example, naturally occurring Cu consists of Cu (69.2%, 7= ) and Cu (30.8%, 7= ). An unpaired electron on a Cu ion couples to Cu and to Cu, giving rise to two, superimposed 4-line hyperfine patterns (in the case of a scalar gyromagnetic factor). As... 

The values for the atomic saturation magnetization at the absolute zero, ferromagnetic metals iron, cobalt, and nickel are 2.22, 1.71, and 0.61 Bohr magnetons per atom, respectively.9 These numbers are the average numbers of unpaired electron spins in the metals (the approximation of the g factor to 2 found in gyromagnetic experiments shows that the orbital moment is nearly completely quenched, as in complex ions containing the transition elements). 

In Eqs. (7-11), fi is the nuclear gyromagnetic ratio, g is the electron g factor, fiB is the Bohr magneton, rGdH is the electron spin - proton distance, co, and cos are the nuclear and electron Larmor frequencies, respectively (co=yB, where B is the magnetic field), and A/fl is the hyperfine or scalar coupling constant between the electron of the paramagnetic center and the proton of the coordinated water. The correlation times that are characteristic of the relaxation processes are depicted as ... 

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