Derivation of the Modified Bloch Equations for Spin Systems

Abstract

A new form of the equations for the time-dependent statistical matrix of a spin system is used to derive the modified Bloch equations, without considering details of the relaxation mechanism. A number of restrictive conditions are imposed on the system, most of which agree well with known limitations of the applicability of the modified Bloch equations. In order to avoid complications, only spins one-half are considered. The theory does not apply to the case where the relaxation is anisotropic but where the constant field and an applied rotating field are comparable in magnitude.