Bloch-Redfield relaxation equation

The relaxation is described exactly by Redfield s operator,23 which allows the relaxation between any two functions within the spin system. The following simplified equation based on the Bloch equations can be used instead of it as well8 ... 

Several formalisms have been applied to relaxation in exchanging radicals. Principal among these are modifications of the classical Bloch equations (8, l ) and the more rigorous quantum mechanical theory of Redfield al. (8 - IJ ). When applied in their simplest form, as in the present case for K3, both approaches lead to the same result. Since the theory has been elegantly described by many authors (8 - 12 ), only those details which pertain to the particular example of K3 will be presented here. Secular terms contribute to the ESR linewidth (r) and transverse relaxation time (T ) by an amount... 

Equation (5.8) may be expressed in the matrix representation using the eigenket basis of the Hamiltonian Hq by following Redfield s treatment [5.4], which is closely related to a treatment of relaxation due to Wangsness and Bloch [5.7]. For a system in the ensemble of N identical spin systems, its wavefunction in a pure state is given by Eq. (2.3),... 

One of the first fields where the quantum nature of the underlying system carmot be ignored, simply because there is no classical limit, is that of NMR. This is also a field where decay is directly observed in spin relaxation back to equilibrium. By giving a radio frequency pulse to an equilibrium system of spins, these are brought out of equilibrium, and, after the pulse, decay back to the equilibrium state. This free induction decay was first modeled phenomenologically by the Bloch equations, which pointed to the existence of two relaxation times, commonly called Tj and T2, but at a later stage Redfield used the density operator formalism to... 

The simplest close-form description of the relaxation enhancement is achieved if the second order perturbation theoty of Bloch-Wangsness-Redfield (BWR) " is applicable. The starting equation for the BWR description is the second order perturbation formula for the evolution of the spin density matrix ... 

---