Spin Part of the Hamiltonian

As in atoms, relativistic terms due to the interaction between the spin and orbital angular momenta of nuclei and electrons of the molecule must be added to the electronic Hamiltonian. There is also a magnetic interaction energy created by the orbital motion of the electrons and the rotational motion of the electrically charged nuclei. The relativistic effects consist mainly of three parts  

Interaction between the spin and orbital angular momenta of the electrons, 

Interaction between the electron spin and the rotational angular momenta of the nuclei, HSR = spin-rotation operator. 

Interaction between the spins of different electrons, Hss = spin-spin operator. 

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The spin part of the Hamiltonian in the solid is identical to that of the AX system, and the solution is the same—a pair of lines for A and a pair for X, as in Fig. 6.2. However, the separation is dependent on orientation of the vector r joining the spins relative to B0, because the effective coupling is D(3 cos2 0—1), rather than D alone. As indicated in Fig. 7.2, the lines cross as 0 is varied, becoming coincident when 0 = 54.7°, the angle for which the term (3 cos2 0 — 1) = 0. This angle that will appear frequently in our later discussion. 

Where the Cartesian components of the spin part of the Hamiltonian read ... 

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