On the reduction of a problem in magnetic resonance

Abstract

The problem in question is to find the motion of an atom having arbitrary spin J in a strong oscillating magnetic field and a static field whose component perpendicular to the oscillating field is small (case B). It is shown how to relate this problem to that of ordinary magnetic resonance–an atom in a small oscillating field perpendicular to a strong static field (case A)–by applying to each case a suitable transformation. In the transformed frames the dominant terms in the equations of motion are equivalent and subsidiary terms are similar, so that results well-known in case A may be taken over to case B. The dominant terms in case B describe a set of resonances whose line-shapes are given explicitly for a particular example. Subsidiary terms lead to shifts of the resonances analogous to the Bloch-Siegert shift. The leading term s in these shifts are given. Terms of higher order may be calculated by employing a technique due to Shirley which is described.