Gyromagnetic factor

At this point, it is appropriate to present a brief discussion on the origin of the FC operator (d function) in the two-component form (Pauli form) of the molecular relativistic Hamiltonian. Many textbooks adopt the point of view that the FC is a relativistic effect, which must be derived from the Dirac equation [50,51]. In other textbooks or review articles it is stressed that the FC is not a relativistic effect and that it can be derived from classical electrodynamics [52,53] disregarding the origin of the gyromagnetic factor g—2. In some textbooks both derivations are presented [54]. The relativistic derivations suffer from the inherent drawbacks in the Pauli expansion, in particular that the Pauli Hamiltonian can only be used in the context of the first-order perturbation theory. Moreover, the origin of the FC term appears to be different depending on whether one uses the ESC method or FW transformation. 

The gyromagnetic factor is twice as large as that appearing in the relation between the electron orbital angular momentum L and the associated magnetic dipole moment ... 

Let us stay within the Dirac theory, as pertaining to a single elementary particle. If, instead of an electron, we take a nucleus of charge +Ze and atomic mass M, then we would presume (after insertion into the above formulas) the gyromagnetic factor should be y = 2H —... 

Also, the gyromagnetic factor for an electron is expected to he ca. 1840 times larger than that for a proton. This means that a proton is expected to create a magnetic held that is ca. 1840 times weaker than the field created by an electron. 

And what about the heavier brothers of the electron, the muon and taon (cf. p. 327) For the muon, the coefficient in the gyromagnetic factor (2.0023318920) is similar to that of the electron (2.0023193043737), just a bit larger and agrees equally well with experimental results. For the taon, we have only a theoretical result, a little larger than the two other brothers. Thus, the whole lepton family hopefully behaves in a similar way. 

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). 

Sk ( t) gyromagnetic factor of R atom (T atom) Mj T subnetwork magnetization... 

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... 

Figure 4.40 shows the EPR spectra for two isotropic systems in which the unpaired electron interacts with two " N nuclei (7= 1). (a) Use Fig. 4.40a to calculate the gyromagnetic factor of the paramagnetic species if the spectrum was measured at 9.75 GHz. (b) Which EPR spectrum in Fig. 4.40 indicates the interaction of the unpaired electron with two equivalent nitrogen nuclei (c) Calculate the values of the hyperfine coupling constants for both cases in Fig. 4.40. 

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