Incoherent Spin-State Mixing

We have thus far considered coherent processes that take place in RPs (which in some cases been have been modulated by stochastic motion). However, the common spin-lattice and spin-spin relaxation processes familiar from magnetic resonance also come to bear on the dynamics of RPs. Typical values of Ti and T2 for small organic radicals in homogeneous solution are on the microsecond timescale and as such are rather slow relative to coherent mixing and RP diffusion. Thus, for the most part, effects of incoherent spin relaxation are not manifest in such reactions. However, for reactions in which the RP lifetime is substantially extended, for instance, by constraining the RP inside a microreactor such as a micelle (many examples in Ref. 14), relaxation effects become significant. 

The curve exhibits three distinct regions of differing field sensitivity. For typical fields produced by static and electromagnets, the field dependence is dominated by the field saturation observed in the middle region of the curve and fields of this magnitude are most sensibly employed to determine if a reaction is field sensitive or not. 

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In the previous section, we learned how the recombination probability of a radical pair depended on the coherent mixing of the spin states caused by the S-To mixing. On the other hand, it also depends on the incoherent mixing caused by transversal and longitudinal relaxation. In this section, we will show that one can obtain a qualitative understanding of these effects by considering the spin evolution described by the Bloch equations. From textbooks of Quantum Mechanics, any Hermitian operator F has the following property ... 

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