Theory of Spin Resonance and Relaxation

Abstract

A quantum-statistical-mechanical theory of spin resonance and relaxation is presented, which avoids the assumptions of earlier theories, is capable of extension to other than the lowest Born approximation for the strength of the relaxation mechanism, and is applicable over a broader range of physical situations. From the Liouville equation for the combined system of spin+bath, the theory yields a non-Markoffian equation for the time development of the statistical density operator for the spin system alone. Detailed consideration is given to the response of the spin system linear in the driving field, and an equation for the steady-state spin density operator is deduced. A simple application exemplifies the new features of the theory and it is shown that it describes the phenomenon of "motional" narrowing. The response to an arbitrary external field is studied with particular reference to the problem of approach to thermal equilibrium and the phenomenon of spin resonance saturation. The latter is considered in some detail for a system of independent spins, for which an equation for the steady-state magnetization is derived and discussed.