Nuclear spin-dependent transition probabilities

Pairs may undergo transitions between singlet and triplet states with nuclear spin-dependent probabilities in the time between successive encounters. 

Nuclear relaxation rates R are related to spin transition probabilities. When determined by the paramagnetic center, they depend on the square of the interaction energy between the nuclear and electron spins and on a function of the correlation time Tc, which describes fluctuations in the interaction energy. The contact contribution is described by (Abragam, 1961 Bloembergen, 1957 Solomon and Bloembergen, 1956)... 

Under conditions of proton decoupling there are two relaxation parameters of general interest the longitudinal relaxation time, and NOE, the nuclear Over-hauser enhancement. The third relaxation parameter, T2 or spin-spin relaxation time is not readily measurable for in decoupled systems. Both and NOE are directly related to the transition probabilities associated with nuclei changing energy levels. However, their functional dependence on transition probabilities differs and they can therefore be used in combination to resolve ambiguities. NOE has been found to be a very sensitive measure of mobility of carbon atoms of proteins and to provide reliable qualitative measures of the state of carbon atoms [3]. 

The relative areas of the absorption lines are proportional to the probabilities of the corresponding transitions. These probabilities depend on the multipolarity of the nuclear transition, initial and final spin states, and orientation of the quantification axis with respect to the wave vector of the y-ray. 

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