On the Theory of the Magnetic Resonance Method of Determining Nuclear Moments

Abstract

Two refinements of the theory of the resonance method of determining magnetic moments as given by Rabi are considered quantitatively: (1) A correction is included because of the fact that an oscillating, rather than a rotating, field is used, (2) the "end effect" pointed out by Millman is taken into account. The results caused by (1) agree with those found by Bloch and Siegert, but the method of calculation is simpler. In the case of (2), it is shown that, under assumptions which mean that the effect is small, and which are usually well satisfied in practice, the effect can be worked out without making more than very general assumptions as to the nature of the field in the end regions. Results are given for the displacement of the maximum, and the asymmetry in the curve, which depend on the sign of the magnetic moment. The sign of the displacement is in agreement with experiment, but that of the asymmetry is not; the discrepancy can, however, be explained when account is taken of the inhomogeneity of the velocities in the beam. The effects increase as the square of the amplitude of the oscillating field.