Magnetic Resonance for Nonrotating Fields

A treatment of the magnetic resonance is given for a particle with spin ½ in a constant field $H_0$ and under the action of an arbitrary alternating field with circular frequency $\omega$ perpendicular to $H_0$. A method of finding a solution, valid at any time, is given which converges the better the smaller the deviations from a rotating field or the larger $H_0$. It is shown that in the lowest order correction the shape of the resonance curve is unchanged but that it is shifted by a percentage amount $\frac{{H_1}^2}{16 {H_0}^2}$ where $H_1$ is the effective amplitude of the oscillating field. This also involves a correction in the values of the magnetic moments thus obtained towards smaller values which however in all practical cases is negligibly small.