Frequency Shifts in a Motional Field-Averaging System

Abstract

In a motional field-averaging system the experimentally measured resonance frequency of a transition can deviate from the volume-average value of the resonance frequency as a result of nonuniformities in the static magnetic or electric field. This frequency shift can be comparable to the linewidth, and it can occur even when comparing two transitions which are linearly dependent on the field. Since this shift is not necessarily accompanied by a line-shape distortion, it can cause unexpected systematic errors. The shift can even occur in fields which are for the most part highly homogeneous, if the residual high-order field gradients concentrate most of the nonuniformity at the ends of the container. The problem is studied on two levels. First, models are used to illustrate the effects of the inhomogeneous field. These models exhibit many of the important properties of the relaxation and the frequency shift which result from the inhomogeneity, and they provide a guide as to the effects of various parameters. The second approach derives general expressions which give the effect of the inhomogeneous static field on the radiating particles. These expressions are incorporated into the usual uniform-field density-matrix equations to give a more rigorous description of the nonuniform field. The theory is applied to explain experimental results.