Determination of Velocity Distributions in Molecular Beam Frequency Standards from Measured Resonance Curves

Abstract

It is shown that the Ramsey resonance curves for most atomic beam machines can be conceived as depending on two distributions of velocity, ρ(V) and ξ(V), the second being a correction for beam width.An analysis and computer program are described which permit one to obtain ρ, ξ and the nominal microwave power parameter from three or more measured Ramsey resonance curves at properly spaced power levels whose ratios are known. The determination from the functions (ρ, ξ) of bias errors due to second order Doppler shift, cavity phase difference, and cavity pulling is described.The method may also be used to improve an experimentally obtained velocity distribution (i.e., one obtained through the pulse technique); to provide the proper function ξ; and to provide diagnostic checks of the measurement technique and the validity of the model chosen for the transition probability.The method is applied to the NBS frequency standard. Error estimates indicate that it is feasible by microwave power shift measurements to evaluate the total bias error due to the above sources to within one part in 1013.