Zeeman coupling

A more general theory for outer-sphere paramagnetic relaxation enhancement, valid for an arbitrary relation between the Zeeman coupling and the axial static ZFS, has been developed by Kruk and co-workers (96 in the same paper which dealt with the inner-sphere case. The static ZFS was included, along with the Zeeman interaction in the unperturbed Hamiltonian. The general expression for the nuclear spin-lattice relaxation rate of the outer-sphere nuclei was written in terms of electron spin spectral densities, as ... 

An isolated superconducting grain can be be described by the reduced BCS Hamiltonian with the Zeeman coupling to the magnetic field... 

WCEF = B Ol + B Ol + B 0 + B ol the Zeeman coupling with the effective magnetic field, Btzee SiBbJ Hstii and the exchange interaction,... 

The second term, H-z, is the Zeeman coupling between the 4f magnetic mo-... 

ERO ELECTRON NUCLEAR HYPERFINE FIELD ZEEMAN ZEEMAN COUPLING... 

The transition between levels coupled by the oscillating magnetic field B corresponds to the absorption of the energy required to reorient the electron magnetic moment in a magnetic field. EPR measurements are a study of the transitions between electronic Zeeman levels with A = 1 (the selection rule for EPR). 

The coupling constants of the hyperfme and the electron Zeeman interactions are scalar as long as radicals in isotropic solution are considered, leading to the Hamiltonian... 

From accurate measurements of the Stark effect when electrostatic fields are applied, information regarding the electron distribution is obtained. Further Information on this point is obtained from nuclear quadrupole coupling effects and Zeeman effects (74PMH(6)53). 

Pulse techniques, coupled with the observation of the decay of enhancement (Atkins et al., 1970a, b Glarum and Marshall, 1970 Smaller etal., 1971) constitute the most sensitive procedure for detecting CIDEP. Both net and multiplet polarization have been described. As with CIDNP, the former is believed to arise essentially from the Zeeman interaction and the latter from the hyperfine term. Qualitative rules analogous to Kaptein s rules should be capable of development. 

The leading term in T nuc is usually the magnetic hyperfine coupling IAS which connects the electron spin S and the nuclear spin 1. It is parameterized by the hyperfine coupling tensor A. The /-dependent nuclear Zeeman interaction and the electric quadrupole interaction are included as 2nd and 3rd terms. Their detailed description for Fe is provided in Sects. 4.3 and 4.4. The total spin Hamiltonian for electronic and nuclear spin variables is then ... 

Quadrupole coupling, isomer shift Quadrupole tensor, nuclear Zeeman splitting, g values, coupling constants, relaxation times... 

The spin Hamiltonian for a biradical consists of terms representing the electron Zeeman interaction, the exchange coupling of the two electron spins, and hyperfine interaction of each electron with the nuclear spins. We assume that there are two equivalent nuclei, each strongly coupled to one electron and essentially uncoupled to the other. The spin Hamiltonian is ... 

Just like the Zeeman interaction (S B), the hyperfine interaction (.S /) is a bilinear term and its coupling to strain (T S I), which we will call A-strain (also, -strain ), should be formally similar to the g-strain (T S B) just discussed. In the early work of Tucker on the effective S = 1/2 system Co2+ in the cubic host MgO, a shift in central hyperfine splitting was found to be proportional to the strain-induced g-shift given by Equation 9.22 (Tucker 1966). 

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