Exact solution of the parameter identification inverse problem for the Bloch–McConnell equations. Longitudinal magnetization

A two-site magnetic exchange model comprising a set of two linear first-order differential Bloch-McConnell equations is considered. The relaxation and exchange behavior is described using a symmetrical form of the general solution derived in the case of longitudinal magnetization for the zero initial conditions. The inverse problem with limited magnetization information has been solved exactly in an analytical explicit form under mild a priori knowledge about the exchange and relaxation parameters.