Transient Decay of Longitudinal Magnetization in Heterogeneous Spin Systems under Selective Saturation. IV. Reformulation of the Spin-Bath-Model Equations by the Redfield-Provotorov Theory

Abstract Alternative formulations to the conventional Bloch equations for the RF saturation of the solid component in heterogeneous spin systems according to a spin-bath model are derived using the concept of spin temperature as suggested by Redfield and Provotorov. These formulations and the resulting equations derived by the projection-operator technique provide an analytical and explicit solution to the general problem of solid saturation under continuous RF irradiation. Using the Provotorov theory, a set of generalized (non-Markovian) equations of motions is derived. The solutions to these generalized equations approach those of the conventional Bloch formulation at one extreme when the applied RF is weak and the Redfield formulation at another when the applied RF is strong. In short, this development provides a simple alternative which removes the restriction of the lineshape function used to represent the solid component; the latter is well known to be non-Lorentzian, contrary to the tacit assumption made in the conventional Bloch formulation. Experimental verification of the generalized theory is provided by transient and steady-state longitudinal magnetization data acquired from cross-linked bovine serum albumin under selective saturation by continuous off-resonance RF irradiation.