Nuclear spin-orbit coupling

As shown by Fig. 2.9, with the inclusion of the spin-orbit interaction, the observed magic numbers were properly reproduced. The spin-orbit interaction for atomic electrons is a small quantum-relativistic effect. The nuclear spin-orbit coupling is much stronger and results, in addition to relativistic effects, from the spin dependence of the nucleon-nucleon potential. 

For elements with lower nuclear charges than tin, the aj-a2 splitting is smaller because of the reduced spin-orbit coupling. For example for calcium, with Z = 20, the splitting is only about 3 eV and usually unresolved. 

The shell theory has had great success in accounting for many nuclear properties (3). The principal quantum number n for nucleons is usually taken to be n, + 1, where nr, the radial quantum number, is the number of nodes in the radial wave function. (For electrons n is taken to be nr + / +1 / is the azimuthal quantum number.) Strong spin-orbit coupling is assumed,... 

Here and H describe radicals A and B of the radical pair and He the interaction of their electrons. The other terms in equation (15) are H g, the spin orbit coupling term, H g and Hgj, representing the interaction of the externally applied magnetic field with the electron spin and nuclear spin, respectively Hgg is the electron spin-spin interaction and Hgi the electron-nuclear hyperfine interaction. 

We apply this technique to study the effect of the spin-orbit coupling on an NMR shielding tensor and the shielding polarizability of the xenon atom. The shielding polarizabilities are defined as the second derivatives of nuclear shielding constants with respect to an electric field E... 

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

For the heavier elements of the Periodic Table, say the third transition series and the actinoids, the approximation that spin—orbit coupling is so small it can be treated as a perturbation on free-ion terms fails. Spin-orbit coupling rises rapidly with nuclear charge while interelectronic repulsion terms decrease with the diffuseness of the valence electron density of larger atoms. 

Usually the Born-Oppenheimer separation of nuclear and electronic coordinates is assumed and small terms in the hamiltonian, such as spin-orbit coupling, are neglected in the first approximation. Perturbation... 

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