Cross-relaxation Solomon equations

CROSS-RELAXATION (AND CROSS-CORRELATION) SOLOMON EQUATIONS... 

Cross-relaxation and auto-relaxation for a two-spin system is described by the Solomon [6] equation ... 

The last point is about equivalent spins (or like spins as the two protons of the water molecule). Referring to Solomon equations (see (13)), we can notice that, because of this equivalence, the effective longitudinal relaxation rate is obtained by adding the cross-relaxation rate to the specific longitudinal relaxation rate ... 

For a spin-1/2 nucleus, such as carbon-13, the relaxation is often dominated by the dipole-dipole interaction with directly bonded proton(s). As mentioned in the theory section, the longitudinal relaxation in such a system deviates in general from the simple description based on Bloch equations. The complication - the transfer of magnetization from one spin to another - is usually referred to as cross-relaxation. The cross-relaxation process is conveniently described within the framework of the extended Solomon equations. If cross-correlation effects can be neglected or suitably eliminated, the longitudinal dipole-dipole relaxation of two coupled spins, such... 

What the Solomon equations predict is, for example, that the rate of change of Iz depends not only on 7Z - 7°, but also on Sz - Sz and 2IZSZ. In other words the way in which the magnetization on the I spin varies with time depends on what is happening to the S spin - the two magnetizations are connected. This phenomena, by which the magnetizations of the two different spins are connected, is called cross relaxation. 

Consider a two spin- system, with spins / and S relaxation coupled to each other. Relaxation of these two spins in the presence of mutual cross-relaxation is described by coupled rate equations known as Solomon s equations ... 

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