Electric Resonance Transitions in a Tapered Electric Field

In this paper we investigate the broadening of the spectral lines produced by small inhomogeneities in the homogeneous C-field of the molecular beam electric resonance apparatus. To do so, we represent the inhomogeneities as an arbitrary function of time because of the flight of the molecules through the field. The transitions which we investigate occur between states which are the instantaneous solutions of the Stark effect problem in which we neglect the effects of nuclear molecular interactions. We obtain a solution for the probability amplitudes for a transition such that ΔJ=0 and Δm=±1 by considering a linear combination of the solutions for the case in which there are no inhomogeneities. As an example, we consider the inhomogeneity of the C-field as represented by a linear taper. In this case the amount of line broadening depends on the ratio of the amplitude of the taper to the amplitude of the radio frequency field which induces the transitions. Because under optimum operating conditions the product of the rf field and the homogeneous field is kept constant, the inhomogeneities have a greater effect in strong than in weak C-fields. The line broadening, however, is considerably smaller than one might estimate from the energy level difference computed for two perfectly hodogeneous fields having respectively field intensities equal to the two extreme values of the tapered field.