Zeeman energy exchange

One of the few advantages of the weak exchange interactions present in most lanthanide systems is that the Zeeman energy associated with typical laboratory... 

Caspers relation r of Eq. (62) is in fact equal to the r12 of Eq. (64). But this author essentially looks for a closed equation for Mt without going into the details of the description of the energy exchange between the Zeeman coordinate and the dipole-dipole system. He therefore confuses r12 with the spin-spin relaxation time. 

The longitudinal relaxation also called spin-lattice relaxation is induced by a quasi-resonant exchange which occurs between the Zeeman energy of the spin system and the thermal energy of molecules which carry nuclear magnetic dipoles. The condition of quasi-resonant exchange of energy is used to calibrate the time scale of relaxation of molecular... 

The first two terms represent the anisotropy energies of the R and T sublattices, respectively. The third term describes the R-T exchange interaction with the intersublattice molecular-field coefficient rt. The last term represents the Zeeman energy in an external field. The equilibrium positions of Af r and Mi can be obtained by minimizing eq. (42) with respect to 0r,0r. However, due to the complexity of this equation, this has to be carried out numerically. 

Cross-relaxation at the nematic-polymer interface. The liquid crystal protons and the polymer protons constitute a two phase proton system. The cross-relaxation at the boundary leads to an exchange of Zeeman energy between the two phases and couples their spin-lattice relaxation rates [202]. Cross-relaxation affects all molecules in the droplet if the exchange of molecules at the surface is so fast that within the spin-lattice relaxation time each molecule in the droplet takes part in this process. For this to take place, both the time required for a molecule to diffuse from the inside of the droplet to the surface Tog, and the time Tg for which the molecules remain anchored at the surface must be short compared to the spin-lattice relaxation time Ty. In the limit of very rapid cross-relaxation (k > (Tf(Tf )p) both phases relax with the same relaxation rate which is an weighted average... 

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