G-factor nuclear

Spin-orbit coupling, g-factors, nuclear quadrupole splitting, hyperfine interaction are some of the magnitude affected by the Ham effect and one can say that Ham s papers have opened up the wide field of the different spectroscopic techniques to investigate the JT effect. 

Density matrix of order k Electronic g-factor Nuclear g-factor... 

Rotational g Factor. Nuclear Spin-Rotation Coupling Constant C in kHz... 

In equation (bl. 15.24), r is the vector coimecting the electron spin with the nuclear spin, r is the length of this vector and g and are the g-factor and the Boln- magneton of the nucleus, respectively. The dipolar coupling is purely anisotropic, arising from the spin density of the impaired electron in an orbital of non-... 

If the atom has nonzero nuclear spin /tlien F = S + I substitutes for S in equation (Cl.4.49), tire g-factor generalizes to... 

Ml = 3/2 than for mj = 1/2. Moreover, the ground state experiences pure Zeeman splitting A M.g 4s given by (4.48) (recall, the nuclear g factor of the 7g = 1/2 ground state is different from that of the L = 3/2 excited state). 

If the electric quadrupole splitting of the 7 = 3/2 nuclear state of Fe is larger than the magnetic perturbation, as shown in Fig. 4.13, the nij = l/2) and 3/2) states can be treated as independent doublets and their Zeeman splitting can be described independently by effective nuclear g factors and two effective spins 7 = 1/2, one for each doublet [67]. The approach corresponds exactly to the spin-Hamiltonian concept for electronic spins (see Sect. 4.7.1). The nuclear spin Hamiltonian for each of the two Kramers doublets of the Fe nucleus is ... 

Fig. 4.15 Effective nuclear g values for the excited I = 3/2 state of Fe in units of the corresponding nuclear g factor (g e = —0.10317). The left panel shows the Zeeman splitting of the 7 = 3/2 manifold with large quadrupole slitting under the influence of a weak field, and the two panels on the right show the 77-dependence of the corresponding effective nuclear g values for the I m/ = 1/2 and m/ = 3/2) doublets with the field oriented along the x, y, and z principal axes of the EFG...

Apart from the already mentioned (Sect. 7.6.1) determination of the nuclear g-factors of W through Mossbauer measurements with tungsten diluted in an iron foil [225, 229] where a hyperfine field at the W site of 70.8 2.5 T was... 

Since in general the nuclear g factors are different for ground and excited states of a Mdssbauer nucleus, the spin state must be quoted when giving numerical values for A in energy (which, however, is usually not necessary for NMR spectroscopy or other ground-state techniques). Thus, for a comparison of A values obtained from Mdssbauer and NMR or ENDOR spectra, usually the ground state is considered. 

The ground- and excited-state magnetic moments ji are tabulated as /ig = 0.09062(3) n.m. (nuclear magnetons, /i ) and jig, = 0.1549 n.m., respectively (see Table Properties of Isotopes Relevant to Mdssbauer Spectroscopy provided by courtesy of Professor J. G. Stevens, Mdssbauer Effect Data Center, cf. CD-ROM). Considering that nuclear magnetic moments are given by the relation p, = giPj I, the nuclear g factors for Ee with /g = 1/2 and 1 = 3/2 are gg = 0.09062 X 2 and ge = 0.1549 x 2/3. With these values and taken from... 

In Equation (6) ge is the electronic g tensor, yn is the nuclear g factor (dimensionless), fln is the nuclear magneton in erg/G (or J/T), In is the nuclear spin angular momentum operator, An is the electron-nuclear hyperfine tensor in Hz, and Qn (non-zero for fn > 1) is the quadrupole interaction tensor in Hz. The first two terms in the Hamiltonian are the electron and nuclear Zeeman interactions, respectively the third term is the electron-nuclear hyperfine interaction and the last term is the nuclear quadrupole interaction. For the usual systems with an odd number of unpaired electrons, the transition moment is finite only for a magnetic dipole moment operator oriented perpendicular to the static magnetic field direction. In an ESR resonator in which the sample is placed, the microwave magnetic field must be therefore perpendicular to the external static magnetic field. The selection rules for the electron spin transitions are given in Equation (7)... 

Here, /3 and / are constants known as the Bohr magneton and nuclear magneton, respectively g and gn are the electron and nuclear g factors a is the hyperfine coupling constant H is the external magnetic field while I and S are the nuclear and electron spin operators. The electronic g factor and the hyperfine constant are actually tensors, but for the hydrogen atom they may be treated, to a good approximation, as scalar quantities. 

The effective hamiltonian in formula 29 incorporates approximations that we here consider. Apart from a term V"(R) that originates in nonadiabatic effects [67] beyond those taken into account through the rotational and vibrational g factors, other contributions arise that become amalgamated into that term. Replacement of nuclear masses by atomic masses within factors in terms for kinetic energy for motion both along and perpendicular to the internuclear axis yields a term of this form for the atomic reduced mass. 

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