Spin-orbit interaction various electrons

Consideration of the spin-orbit interaction and the effect of an external magnetic field on the electronic ground state of an ion in a CF allows evaluation of the various terms in the spin-Hamiltonian of Equation (31). In addition, the interaction of the nucleus of the paramagnetic ion and ligand nuclei with the d-electron cloud must be considered. In this way the experimentally determined terms of the spin-Hamiltonian may be related to such parameters as the energy differences between levels of the ion in the CF and amount of charge transfer between d-electrons and ligands. 

In this section formulae are given for the algebraic matrix elements of the electrostatic and spin-orbit interactions between antisymmetric functions of various electronic configurations characteristic of the rare earth spectra. All these formulae were constructed in the ySLJM coupling scheme. ... 

The above method of approach was first proposed by Van Vleck concerning the susceptibility of ferricyanides, and detailed treatments have been given by Howard and by Kamimura for the complexes. This procedure has been developed by Kotani to account for the temperature dependence of the susceptibilities of various low-spin compounds. Griffith recently extended Kotani s calculation to the high-spin compounds. For Ad and 5d metal ions, the spin-orbit interaction is much stronger than the 3d electrons and has the comparable order of magnitude with the Coulomb repulsion.Susceptibility calculation for these group... 

The indirect electron spin-spin coupling may also be analysed in terms of spin currents (Problem 11.17). Briefly, one spin dipole produces, via the spin-orbit interaction, small circulating currents around the various nuclei, the currents being different for up-spin and down-spin components the resulting spin polarization is picked up by a second spin and leads to the tensor interaction already derived. 

Reference values for the various 2-component relativistic Hamiltonians are provided by the 4-component Dirac-Coulomb Hamiltonian, but we have also included orbital energies obtained with the Dirac-Coulomb-Gaunt (DCG) Hamiltonian. As already mentioned, the Gaunt term brings in spin-other-orbit (SOO) interaction. Since spin-orbit interaction induced by other electrons will oppose the one induced by nuclei we see from Table 3.3 that the spin-orbit splitting of orbital levels is overall reduced. However, one should note that the Gaunt term also modifies /2 levels. 

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