Magnetic Resonance for Arbitrary Field Strengths

Abstract

Starting from a microscopic viewpoint, the steady-state value of the magnetization of a system of moments has been calculated semiclassically and quantum mechanically when the external field has a circularly polarized component perpendicular to the constant component. It is assumed that the only other processes which can change the orientation of the individual moments are strong collisions, and that their average tendency is to produce equilibrium with respect to the instantaneous value of the field. The solutions thus obtained predict a nonzero absorption in zero constant field, and that there is no dependence of $g$-values on frequency. Further properties of the solutions are discussed. It is also shown that the solutions for the circularly polarized case, as well as Garstens' expression for the absorption coefficient for the linearly polarized case, can be obtained as steady-state solutions of the macroscopic equation $\frac{d\mathrm{M}}{\mathrm{dt}}=\gamma \mathrm{M}\times \mathrm{H}+{\tau }^{-1\mathrm{}}[{\chi }_0\mathrm{H}-\mathrm{M}].\mathrm{}$ This equation is a special case of an equation in which longitudina relaxation is assumed to be along and transverse relaxation perpendicular to the instantaneous field. The relation of these results to the question of the general validity of this modified form of Bloch's equation is discussed.