A General Theory of Magnetic Resonance Absorption

A general expression for the frequency-dependent susceptibility of a magnetic system is derived by a quantum-statistical method based on the linear theory of irreversible process. This fundamental equation provides a physical ground for the so-called Fourier transform method for computing the resonance line contour. The auto-correlation function, or the relaxation function of the magnetic moment, that is the Fourier transform of the absorption intensity distribution, can be expanded in terms of the perturbation energy, which is assumed to be responsible for changes of the resonance spectrum from the unperturbed distribution. A general method is shown how to choose from the expansion terms those which contribute to a particular line of interest. This is a generalization of the method of using projection operators. The customary moment method is examined from this point of view. Introducing a further assumption, we propose a method for computing the contour of resonance lines from the obtained expansion. This may be regarded as the quantum-mechanical formulation of the idea employed by Anderson and Weiss for the exchange narrowing problem of paramagnetic resonance. The problem of motional effect on the broadening is treated from this. general point of view. Particular applications of the theory to the motional effect of the dipolar broadening in nuclear magnetic resonance and to the exchange effect in paramagnetic cases are also discussed in detail. Some basic equations such as used by Bloembergen, Purcell and Pound for nuclear magnetic case are reexamined and corrected.